The Utah law does address some of the issue of liability for the owner of stolen weapons as long as they were properly stored. It does not protect the owner of the lot for having failed to preclude the theft. I don't know how they are going to specify what constitutes proper storage without playing favorites; that looks like a regulatory black hole.
The UT law distinguishes parking lots with security measures from those that do not (interesting additional considerations there), if I read it correctly, by allowing the guy with a fence to ban the weapons presumably because he's protecting life and limb by other means (interesting equal protection consideration there given that the government permits or denies what constitutes an adequate fence in the first place for the purposes of the statute (another black hole)).
From what I can tell, there is nothing in the UT law that addresses the liability of the lot owner for secondary damages due to stolen weapons, or for having failed to verify that they are properly stored in the car. Those liability protections are only extended to the gun owner.
I know that sounds kinda extreme as a case, but remember, I live in California. In this state, if a guy goes on a roof to break into your building and falls through a skylight while trying to break it in order to gain entry, the building owner is liable for not having built an unbreakable skylight, despite the fact that it was built to standards set by that same government.
If the parking is considered to be "secure" i.e. with fence and guards, a citizen is not allowed to keep a gun in his car, and must submit it to secure storage at the liability and responsibility of the secure lot owner. I believe case law will in support the reasonable goal of this statute. They have in the past, but anything's possible I guess.