Alan Dershowitz believes Liz Cheney will become a Democrat and run against Trump

And I can pretty much guarantee she would lose in that case. Right now it looks like she can't even hold her Senate seat

Doubt it. The Democratic Party won't embrace her. She's too conservative. If she runs, I suspect it will be as a Republican (less likely) or Independent (more likely). She won't win, but her primary goal seems to be keeping Trump from winning.

She might as well switch, but to be honest I don't think she could beat out Biden, she is not that popular.