It's important to qualify this: jet fuel contains no lead, and constitutes the vast majority of commercial aviation, and hence of emissions.
Jet fuel itself is kerosene, with some additives that aren't superb in raw form, but nothing so durable in the environment as lead.
A sibling comment does a fine job of explaining why avgas still contains lead, and to be sure, a plan to phase that out except where absolutely necessary would be welcome.
The issue is infrastructure. Modern engines run fine on unleaded fuel, but the little airstrips in the middle of nowhere all have 100LL and/or jet fuel, so that's what pilots use.
I know a few pilots who are prefer to use unleaded in their Rotax engines to prevent spark plug fouling, and they have to jump through some pretty ridiculous hoops to get gas, while their buddies just fill up with whatever is on the field.
It seems you would try methane before you try hydrogen:
https://energynews.us/2013/08/26/midwest/could-natural-gas-f...
Petroleum-based liquid fuels contain mixed entity hydrocarbons that match a specification; if you have the perfect feedstock and markets for the fractions you don't use this is cheap. Worst-case you have to synthesize them with Fischer-Tropsch chemistry
https://en.wikipedia.org/wiki/Fischer%E2%80%93Tropsch_proces...
which is such a PITA (normally a chem E would be delighted that you can use iron as a catalyst, but it works so poorly that a desperate search of the other 91 elements found just 2 that sorta-kinda work)
The issue there is you are sticking C's onto the end of a chain and you have to deal with a network of reactions that produce products you couldn't care less for, such as petroleum jelly that gums up your catalyst, sticks up your downrisers, etc.
Sustainable motor fuels tend to be single entities such as 1-butanol, dimethyl ether, etc. You might need to blend something in for low temperature starting, but it's possible for a single entity fuel to be synthesized with decent yield.
General av is seen as a backwater that is barely hanging on and couldn't possibly get the lead out. The USAF has done biofuels trials, but commercial av is spooked to try anything that could leave passengers up in the air.