IANAL, but I think all lawsuits and appeals would need to be expedited on an emergency basis, argued, and decided (or simply dismissed) before we start running into federal and constitutional deadlines.
Certainly, any legal issues remaining after January 6, 2021 (or whenever Congress certifies the electoral college vote) would likely be dismissed as moot. Recall that the U.S. Supreme Court actually stopped the recount in Florida in 2000 because they were approaching these deadlines.
Upcoming federal deadlines are here:
December 8, 2020: The “Safe Harbor” Deadline (deadline for states to resolve any controversies with their elections in order to avoid congressional second-guessing when electoral votes are counted)
December 14, 2020: Electors Vote in Their States
January 6, 2021: Joint Session of Congress to Count Electoral Votes and Declare Election Results Meets