trust me, there will be republican lawsuits galore.
The lawsuits can't be based on ballot deadlines for November because the Democrats haven't even nominated their candidate yet.
The basis of the lawsuits will almost certainly be on state primary election rules about candidates. Basically, all fifty states held primary elections that cost a lot of money to administer. And each state has its own laws that govern the process once a candidate wins the primary.
I would not be surprised if some -- maybe many -- states have laws the prohibit a candidate from appearing on its general election ballot if the candidate did not run in the state's primary.