What is time requirement in Utah for landlord to notify tenant of nonrewal of lease

That's usually specified in the lease. Utah doesn't seem to cover this specifically (or I just can't find it.). It does require at least 15 days notice prior to the end of the rental period for month to month tenants.

Does your lease not specify?

Assuming nothing in the lease, I don't think the LL has to give such notice. Without notice from either party, it becomes a tenancy at will.

What's the specific situation? Are you the lessor or lessee? Has notice been given and, if so, when in relation to the lease expiration date?