So I have two traditional PL desk lamps, both have one 11w PL-S bulb. (Lival Global & Airam Campus)
What I noticed today, is that whenever I turn on or off either one of them, my monitor tends to go black for a second. After that, it turns back to normal. My monitor is an external one (connected to my laptop with a cable), and nothing else is going off. What is causing this? Everything is in the same extension cord and grounded.

Here is another similar situation: once I was in my grandparents' home, I brought this Glamox light with me. Whenever I turned it off there, their television went completely black for a while! Only differences are that they were located in different rooms and not grounded.

Either the lamps or the TV or monitor aren't properly protected against (causing) RF interference.

Any device that creates an electric spark, creates radio waves. That is literally how the radio transmitter was invented. The first radio transmitters were giant transformers and coils, with a spark gap to create tremendously loud sparks. Little sparks always happen when turning on or off a fluorescent lamp with inductive ballasts, and the starter itself also can function as an RF impulse generator.

Any device sold in western countries has to meet quite strict regulations to avoid a simple desk lamp working as a radio transmitter. And conversely, any consumer device needs to be tolerant to RF interference up to a certain level. Cables, however, are not usually held to any standards.

If your desk lamp meets the regulations and only creates a small interference pulse, but your TV is overly sensitive, the TV is the problem.
IF both meet regulations, the cable might be the problem.
If it is 'grey' import from china, that device is highly unlikely to meet any RF interference specifications. That goes for almost everything you buy there, from LED bulbs to RF ballasts to phone chargers. Many aliexpress/temu/amazon products are extremely bad in that regard. Ironically, the charger of my Baofeng amateur transmitter interferes heavily on my AM radios. Meanwhile, i can use my laptop charger right next to them. Both are made in China - that's not the issue - it's the lack of proper engineering and quality control for the grey import ones.

And finally, over the course of decades of use, sometimes interference suppresion capacitors - even the ones that don't just violently burn out like a Wima or Rifa - fail. That has no effect on how well your lamp works, but now it does create significant interference pulses that can interfere with any kind of electronic device, if you're unlucky.

How to solve? Firstly, it's always best to tackle the root cause. Use an interference suppresion filter at the device that causes the interference. If that device already only barely interferes, the TV cable might have insufficient shielding. I've heard HDMI is particularly sensitive to interference, despite being a digital format.

Always make sure that devices that have a grounded plug, are also really plugged into a grounded outlet.

Yup, it's interference.
My monitor displays a horizontal line when turning on the fan, or when switching between the low and high settings, they're both plugged into the same UPS.
Then the desk lamp generates an insane amount of interference that will make the radio only play static, it's an older receiver and the lamp has a pretty crude external power supply, there might be better options that don't cause any interference but this was the only one I could find for the wattage output I need.

Try using different wall sockets.

To me it seems like a [unpublishable] cable with improper shielding or improper connection, the data transfer loses synchronization. The connection uses symmetrical lines internally, but just a LVDS, so with not that much common mode range and barely 200mV signal, so the signal gets corrupted if any spike larger than about 1V gets on the lines. The shielding and mainly laptop-monitor "ground" connection the shielding provides is quite essential there. Normally, without any external disturbance, the link uses to work even without the shield, but it is then extremely sensitive to any disturbance, so there are many cheepeese "cables" that are lacking that shield, as it still appears working normally when "tested".
Or the ground/shield connection could be bad within the connector assembly of the laptop or the monitor.