Lead was not a top end "lubricant" nor was it's environmentally safer replacement as such, it acted more like SCA's in diesel coolant. The lead (and now the "green" additives) coated the exposed surfaces of the valves when burned. This coating was beaten off the surface as the valves opened and closed instead of the valve and valve seat material being impacted.
When an engine that was meant to be run on leaded gas is run on unleaded gas that protective barrier on the valves and seats is not present. The closing valves come into direct contact with the unhardened valve seat material and a bit of seat material is transfered to the valves and is lost the next time the valve cycles. This leads to valve seat recession into the head or in the best case just uneven seat facing which causes poor sealing. "Burned" out valves are a result of exhaust gases that are excessively hot which weakens the valve itself. Portions of the vales can actually break off and cause a dead miss on that cylinder.
Gasoline engines need very little lubrication from the gas. Really the only thing lubed by the gas is the pump and with modern electric pumps that is really not much of a concern. I've found that heat is more of a problem for the fuel pump than lubricity. The in-tank pumps are cooled by immersion in the tank. People who consistently run the tank to near empty put many hours of time on the fuel pump when it is partially/fully above the fuel line in the tank. Eventually the (usually) composite components distort and stop pumping fuel.
Ethanol has some major disadvantages, imo. In older vehicles ethanol has a tendency to rapidly decay fuel system seals due to an incompatibility with materials used in these fuel systems. Ethanol is less resistant to ignition so it has a tendency to cause pre-detonation. Modern fuel systems can correct for this, usually by retarding the ignition timing which reduces power output. The heat value with ethanol is lower than gas which means it takes more volume of ethanol to produce the same power output as gas which results in lower MPG. Ethanol has some advantages for emissions purposes and to reduce petroleum dependence.
That is one reason I like biodiesel so much. It is the best alternative fuel that has been developed so far. It doesn't significantly reduced power output (I lost about 12 HP on the dyno at full load) and has better emissions overall than petro diesel. It is actually safer than petro diesel and has incredibly high lubricity values compared to petro diesel.
Ok, I'm almost done (takes one foot off soapbox).
I haven't ever run a lubricity additive in gas engines. I have run a lead additive, or sourced tetra-ethyl lead for use in older engines, however I've replaced all of the unhardened valve seats so I'm just running regular unleaded. The only additives I see any reason to put in gas is something to clean valve and piston deposits. With modern engines with very closely monitored fuel systems engine deposits such as carboned valves take quite a while to occur, so I don't use cleaner adds very often either.
If you wanted to run a 2 stroke oil in a small quantity I would say that is fine, although it's not doing much, if anything, to increase the longevity of a gas engine. If you are running ethanol blended gas there isn't much to do other than switch types if possible. Ok, I'm really done now, no really I am.