Possibly (Andretti has a lot of class and might be willing to forgive the authorities enough to try again next regulation change), but that's not even in the top 3 sets of lawyers that most concern me, that would potentially be interested in it.
1. The FIA backed by EU anti-competition lawyers (commercial promoter taking a decision openly on the grounds of something that is specifically within the FIA's capacity, which has been prohibited by legal settlement since 2001. Since Andretti being refused an entry reduces the competitiveness of F1, and F1 is a de facto monopoly at its tier of single-seater motorsport, the FIA would have a strong case here - if only to prevent a counter-suit that broke the FIA's monopoly altogether. Effect: Winning such a case would give the FIA the authority to kick out Liberty, appoint a different commercial promoter and invite Andretti back to the grid).
2. Felipe Massa's legal team (further evidence that commercial and regulatory interests cannot be extricated in F1 in practise, despite a legal requirement via settlement to separate them. Effect: makes Bernie's interview with a tabloid last year a stronger basis to allege wrongful manipulation of the 2008 season. Converting the civil case to a criminal one opens the possibility of changing the 2008 season result based on the victory being classed as "stolen goods" that can be forcibly taken back by courts rather than "misallocated results" that can't. None of this would help Andretti get into F1, but might make it feel better about being declined).
3) Shareholders in Liberty. I'm not convinced that this decision is in their best interests. It's possible some of them could decide to sue on that basis, whether Andretti's cool with that or not. This would cause less trouble for F1, even if they won, but Liberty should be very concerned.
Alpine would be at risk of quitting at the next opportunity, though don't expect them to sue if they do - it's not their way of doing things.