Yes, you can claim the homestead on your mobile home (manufactured home) even if you just rent the lot below it.
The 10th Circuit Bankruptcy Appellate Panel (BAP) actually ruled on this specific issue in
In Re Carlson, 303 B.R. 478 (10th Cir. BAP 2004) . The court held that:
owning the land surrounding a mobile home is not a prerequisite to claiming the mobile home exempt as homestead under Utah law
In other words, your mobile home is the homestead. It doesn’t matter if you are only renting the lot. At least $42,000 of that home’s equity is safe in bankruptcy! (As long as you are on title for the mobile home).