A lawsuit that claims what, exactly?
There are no Presidential elections in the Constitution.
How about a lawsuit coming from the people who are deprived of voting for President Trump? I understand you have to be hurt some way to file a lawsuit, well, not being able to vote for someone I like is hurting me...and I assume I am not the only one.
There are only three things in the Constitution that qualifies you:
Natural born citizen
35 years old
live in the US for 14 years
Anything else is contrived.