Lightbar power options

[extraordinary_quelea]

Hello all, first time here.
My project is a bicycle fitted with a 14 inch led light bar and an led truck tail light. Both lights can run on either 12 or 24 volt ( possibly something in between?). At the moment I run them off a sealed 12v 3ah battery. A bit bulky for the bicycle, but after 50 minutes I still have 80% power left.
The lightbar is rated at 36 watts, not sure about the tail light. The battery is in the checkerplate box on the seat tube.
So my question is, if I repower with lithium ion or lithium phosphorus for a more compact power source, would I benefit from an 18 volt set up or a 24 volt set up? Would the lights shine brighter? Or would I stick with 12 volts? I was considering trying to use an 18 volt power tool battery pack for ease of charging and the possibility of just swapping batteries. Any thoughts?

 

[Kiwi]

It doesn't matter what voltage you choose as the internal circuitry in the lights will regulate the voltage down to the required level. Brightness will not be affected. The only real difference is that the lights will draw less current on 24v than 12v.
LED lights like these are listed as multivoltage. For automotive applications this means they are suitable for 12v or 24v vehicles. The specs will probably give a voltage range from 8v to 30v.