Sometimes I dial into the automated weather report at the airport. I noticed last year just before a hurricane my local municipal airport recorded a message on their weather report saying "Pilot controlled lighting is now in effect. Click twice to activate runway lighting."

Does anyone know what that means or why it would be put in effect? Does it have something to do with the airport being closed during the hurricane, so there is no traffic controller on duty? Or why would anyone be using the runway during a hurricane?

Yes.  Some airports have a lighting relay connected to a radio frequency.  The pilots will key the mic/transmit button on their radio in a certain pattern (twice is the most common, so.. click click) and that will activate the relay which in turn turns on the runway and and taxiway lighting for a predetermined amount of time (10 minutes in most cases) This is at airports where there is not a control tower or where there is not 24 hour air traffic control.  It is a great way of saving energy. 

It can happen that some plane going by, which was not expected at the airport, will come for emergency landing without advance warning due to the hurricane. They will benefit from the lighting (even if most likely could land without it). They may not know about the lighting switching practice in this airport

What is the argument for switching off the lighting during the hurricane ? Saving few days worth of energy use at most ?

Airports run on strict government rules.  There is no bending the rules.  If the aviation division of a government (FAA for the United States) says that the airport cannot operate unless under certain circumstances, that is the law plain and simple.

They may not know about the lighting switching practice in this airport

In that case they will not know about the airport existence in the first place. If you are heading to some airport, you should be able to know about all the rules there from the same source you have the knowledge about the bare airport existence alone - being that your preflight planning, maps or even from the one responding to your emergency call. In that case the lighting control is the least important knowledge you need there, regardless if it is a normal landing or an emergency, without which you wont be able to land or become very high safety risk for others anyway...

What is the argument for switching off the lighting during the hurricane ? Saving few days worth of energy use at most ?

Many airports are used mainly during daytime and even that barely once a day, cases needing the lights  are not more than once a month. Need to leave the lights on 24/7 would make the lighting way too expensive (not the electricity, but mainly the maintenance) to be installed in the first place, so the options are either no lights at all or allow for such control. As the radio is practically mandatory equipment onboard, there is no problem with that at all. The planes that can operate without the radio should land way before the conditions deteriorate for the need for the runway lighting becomes of any real benefit, so no difference from leaving them ON all time either.

Airports run on strict government rules.  There is no bending the rules

The rules set a minimum requirement. Normally there is no limit on exceeding the requierment

In that case they will not know about the airport existence in the first place. If you are heading to some airport, you should be able to know about all the rules there from the same source you have the knowledge about the bare airport existence alone - being that your preflight planning, maps or even from the one responding to your emergency call. In that case the lighting control is the least important knowledge you need there, regardless if it is a normal landing or an emergency, without which you wont be able to land or become very high safety risk for others anyway...

You can know about the existence of the airport from seeing the runways from the air, especially with the lighting on. Probably atleast on a slower aircraft. (I'd imagine that somebody with a private aircraft might be more likely to get into such situation vs. a commercial airline aircraft)

The chances to hit another plane on the runway, when there are supposed to be none due to the weather, is probably low and could be weighted against the chance of accident resulting from staying any longer in the air. Especially if it can be seen (that there are no signal lights of another plane on the runway)

Many airports are used mainly during daytime and even that barely once a day, cases needing the lights  are not more than once a month. Need to leave the lights on 24/7 would make the lighting way too expensive (not the electricity, but mainly the maintenance) to be installed in the first place, so the options are either no lights at all or allow for such control. As the radio is practically mandatory equipment onboard, there is no problem with that at all. The planes that can operate without the radio should land way before the conditions deteriorate for the need for the runway lighting becomes of any real benefit, so no difference from leaving them ON all time either.

Since the message was given in context to the storm, i understand this as this airport normally having the lighting on all the time, and now changing to on demand operation due to the storm. That makes only a few days of difference in electricity use

If we assume (for example) 1000 50W signal lamps, lighting for a week straight at nights only (8 hours), that is a one-time saving of $400 in electricity. It's tiny fraction vs. typical running expenses of an airport

The rules set a minimum requirement. Normally there is no limit on exceeding the requierment

There is: The expenses. The "JFK intrernational" like airports is very minority.
Most (by counting, not their improtance, nor traffic or size, etc) airports are nothig more than a regularly mowed stripe of grass field framed by the required red-white marking signs (the minimum "equipment" to be officially recognized and published in maps etc).
Even not a single building, even no shed, nor "wind sock" or anything like that at all.
Then a buit less airports have just some shed nearby.
So the cost to run such airport is no more than every two weeks mow the grass andd every other year repaint the marking signs. Not that expensive to operate at all.

You can know about the existence of the airport from seeing the runways from the air, especially with the lighting on.

You would have to be a Superman or it would have to be the "Area 51 main airport" (so in the middle of dark nowhere) to spot it except being few miles away and lined up with the runway. Hypothetically possible, but exremely unlikely if you do not know about its existence from some other source.
The fact you spot it when in a landing airplane is a bit misleading - the pilots had already lined up the plane with the runway because they are heading there, from such angle you may spot it from 10 miles or even more (at night with good weather), but again, the chance to be in that narrow stripe position when you happen to need it is nearly zero.
By the way listening to such automated broadcasting is way more likely a way, how you learn about the airport existence. And there you learn about the operating regime as well.
And even more likely you find that airport in the map, with the frequency of such automated broadcast and all those details you learn from there...

Since the message was given in context to the storm, i understand this as this airport normally having the lighting on all the time, and now changing to on demand operation due to the storm. That makes only a few days of difference in electricity use

I undersood it as the storm triggered the listening to that broadcast.

However there is one good reason for switching to the pilot activated mode in such case: During a storm, there is very high risk of a commercial power outage. So the lighting has then to rely on the backup battery, which provides just a limited runtime for a load such as the lights.
The mode switching can not happen in an unexpected way - because at that moment there culd be someone just landing on it, so it would be quite nasty surprize for him. So the lights are switched to the pilot activated mode upfront when the storm comes scloser, so from now on the lights will burn only for a short time for an aircraft to land, so the batteries can handle that without any glitch regardless when and if the power will drop.

As a pilot, I will tell you the most obvious reason is the most basic, historically; to reduce the amount of wear on the bulbs. Most runway lights that haven't been converted over to LED still run halogen. It's cheaper in the long run to run these at a reduced power. On a clear night there is no reason for the airport lights to be at 100%. This causes unneeded light pollution, energy waste, and can be bothersome for people living close to the airfield. The airport is made to be identified at night with the beacon, and once pilots get closer to the airport for landing, they can elect to turn up the runway lights for better visual guidance. These are usually on a timer, so after a few minutes they go back down to dim. Sometimes at night, while trying to figure out exactly where I am, I will key up the lights of the airport I am nearest to, just to visually verify my position. At larger airports with ATC towers, the tower controls the runway lights depending on the conditions outside. Typically, the worse the visibility, the brighter the runway lights will be. Interestingly enough, even the high intensity strobe "bunny rabbit" lighting is adjustable in brightness, and on a clear night may be used on a very low setting, or not at all.

Boiler What aircraft do you fly ?

Boiler What aircraft do you fly ?

Nothing fancy, fixed wing prop/general aviation. I don't get up nearly as much as used to, but it still remains one of my favorite things to do.