In a word, no.
Old cars weren’t ‘designed’ to use lead. And lead never ‘lubricated’ or ‘cushioned’ anything.
The main problem with cars using unleaded is the fuel had lower octane than before. Oh, the sticker on the pump still said “89 Octane”, but now the unleaded fuel had exactly 89 octane (or even 88.9), whereas before with leaded gas it was often a couple of points higher. That’s because it was cheap and easy to add a bit more lead to guarantee the octane rating. But with unleaded it was much more difficult and expensive just to reach the rating. So cars that ran fine on the old “89” and pinged on unleaded “89” were really cars that needed 91+ octane all along.
The problem wasn’t the lack of lead. It was the lack of octane.
Add if those cars had unhardened valve seats, where seats were cut directly into cast iron cylinder heads, the continuous pinging would result in valve-seat recession. But airplane engines use hardened valve seats. They have to because aluminum is too soft to machine a seat directly.
Getting the lead out will make airplane engines run better, not worse.