Any renewable or nuclear energy source would make it carbon neutral. It doesn't have to be free, the fuel doesn't cost that much in the first place, so a modest percentage cost increase is fine.

We know that making the methane isn't super-expensive, because we've already used the Sabatier process commercially to make methane from CO2. That used carbon-based fuels to get the CO2; to really go carbon-neutral it'd have to be biofuel, or we'd need to pull CO2 from the air using direct-air-capture machines.

https://en.wikipedia.org/wiki/Sabatier_reaction#Creation_of_...

Apparently they already do this or have plans to do this with solar power:

https://twitter.com/elonmusk/status/1258308230725292032