As a civics amateur, the only lame leg I could see an appeal standing on would be something like a 4th amendment equal protection argument. I.e. the law doesn't apply to all cases for all indefinite time, therefore it's "unfair" to those it does NOT protect. That's kind of like protesting a half full glass of water by pouring it out on the ground. But Felos would be slime enough to try it.
something like a 4th amendment equal protection argument. Yes, that is right, and anyone could bring the case. I doubt it will be a party in the action.
Equal separation of power would be another.
The courts have granted the executive branch special powers in matters of life and death however.(for example, the power of parole)
It will be interesting and a new precedent if it happens in this case.