I don't use an L5 but had one that was similar. I think legally you should have the gas turned off while driving.
I don't agree with all the mods etc that nathaneal has made- clever as they are-. Why not just get a more robust and reliable heater?
Mine is heavy on water usage, but is completely safe and utterly reliable.Mine does not have auto ignition (they are all electronic ignition, but the L5 does not have a pilot light because it's automatic, while mine does). From memory mines a Rinnai eu85e and cost £300.Trust me, this is a better option.