Election law is complicated. Even lawyers hedge on these things because it's not as simple as looking up the statute, you have to look up previous court cases, and if it's a case of first impression make a lot of inferences.

Issues I see include whether it is legal to solicit political endorsements which will potentially become campaign materials, in exchange for pay or the prospect of pay, whether it's legal to run lotteries in multiple states (but excluding all others), whether it's legal to influence an election by running such a promotion etc.

The first and second issues make for an interesting combination, because my understanding is that Musk is soliciting people to sign a petition in support of the first and second amendments. Since these are in the constitution of the whole United States, why is his 'lottery' restricted to only 7 states, to the disadvantage of people in the other 43?

Incidentally, Rick Hasen, an election law prof at UCLA, says it's definitely illegal. https://electionlawblog.org/?p=146397

Mr Beast is being investigated for illegal lotteries. Very similar to this. They're not guilty until tried. But it could end up costing both of them quite a bit.