I'm not too sure if the lead helps a 2 stroke with any type of lubricating properties Tetraethylead was originally added to fuel to lubricate and provide a cushioning layer for the valves, an increase in octane was an unexpected side effect of the Tetraethyllead. A 2 stroke only relies on oil for lubrication. The best reasons for running Avgas are the consistency and quality control, no alcohol, availability, and cost.
Riffraff is correct. Light aircraft piston engines need the lead in the valve train to prevent sticking and failures. Might not be a bad idea for that 4 stroke you secretly have hiding in your garage either. As for the lubricating properties in a two stroke, that is debatable. It does not however contain ethanol and undergoes more sampling and testing to ensure its quality. That and it just smells awesome as premix in a 2 stroke. It is usually cheaper than race fuel as well. I pay about +- $5.00 vs +/- $7.00 a gal for race gas.