I was wondering if incandescent is the most inefficient light source, due to 10lm/1w to 15lm/1w. Is there any other light source that I don't know about that has less than 10lm/1w?

Mercury Vapour bulbs are the 2nd inefficient light source, right?

Do you count combustion based light sources? Because my Kosmos oil lamp (which is a good lamp) puts out approximately 250w of power for approximately the same light output as an 15w light bulb.

Furthermore, it's all hard to compare. There were quite inefficient discharge lamps such as CO2 lamps in the late 19th century that were of less efficiency than "today's" high power incandescent lamps. In their own day, they may have been a moderate improvement in efficiency over carbon filament lamps but those things never caught on as general lighting because of the high voltage needed.
Neon runway lighting is on par with your average incandescent lamp.

Then you got those Nernst lamps. I have no efficiency figures for those. Carbon arc lamps are comparable to modern incandescents, but in their day they were much better than carbon filament lamps - not in the least because they offered a very high color temperature combined with power levels that could be cranked up into the kW levels, rather than a dim yellow/orange glow.

Check out www.lamptech.co.uk for actual hard data about various types of lamps that were actually in full scale production. 

There are also incandescent mantle combustion lights, significantly better than old plain flame light sources.

Also there are colored 'flame' carbon arcs doped with metals, which can be thought as metal halide lamps predecessors.

Neon runway lighting is on par with your average incandescent lamp.

Not true!

Do not write off neon sources easily! While plain lm/w figures may look unimpressive, neon red light sources are significantly more efficient in producing red light than filtered general purpose incandescents.

Oh i don't doubt that filtered incandescents are worse. But just lm/w versue lm/w as if we're comparing LPS to HPS or something, makes them about on par.

Do you have any more information about the doped carbon arc lamps? I've never heard about those before but it would be fascinating to read up on them and what those were used for. I'm currently actually experimenting with exactly that, but for the purpose of doing chemical spectrography, rather than producing light.