By all means, let's take the novel approach in this thread of trying to actually answer your question. And, as is so often the very unsatisfying case, the answer depends on state law.
There are basically two issues under state law: (1) state license to carry LTC) rules; and (2) state firearms transfer rules.
In a few States the LTC specifies, by make, model and serial number, the gun or guns one is authorized to carry. I know that's the way it's done in California, and I think New York might be that way as well. In a State like that it would be a violation of the carry laws to carry a gun not listed on one's LTC. I don't know, however, whether an issuing agency would, in such a State, be willing to list a spouse's gun on one's LTC.
As to the other issue, we know now that a loan is a transfer. Therefore, letting a spouse use your gun would be subject to whatever transfer rules apply in your State.
In most States a no formalities are required for a private transfer. Therefore letting a spouse use your gun would be a non-issue (of course assuming that the spouse is not prohibited from possessing a gun).
Some States do require formalities for private transfers. However, as far as I know the transfer laws of such States provide varying sorts of exemptions and exceptions for short term loans or transfers between family members. Unfortunately, the terms and conditions of those exceptions and exemptions differ state-to-state.
The trick in States with transfer requirements will be to understand the terms and conditions for any applicable exceptions or exemptions. I suspect that it would not be difficult to manage letting a spouse use your gun in a way that would satisfy the terms and conditions for any applicable exceptions or exemptions.