SLC Tower Controller reported Aircraft X lost radio contact and deviated from clearance which resulted in an MVA alert and conflict with traffic.

Narrative

I was working local east and city. Aircraft X was inbound from the southwest. I observed them go through the final about 14 miles south of the airport. I called the Approach Controller and they indicated they had lost communication with the aircraft and were attempting to re-establish contact. Aircraft X then came up on my frequency about 15 miles southeast of the airport heading into rapidly rising terrain as well as a VFR aircraft outside the bravo airspace not receiving services. I issued Aircraft X a low altitude alert and traffic alert while climbing them and turning them away from the mountains. Aircraft X was able to get the unidentified aircraft in sight and maintain visual separation. I pointed out the airport; which Aircraft X then had in sight; and cleared them for a visual approach. Aircraft Y was on an approach to Runway XXL which Aircraft X was able to get in sight and maintain visual separation from. Aircraft X then landed with no further issue.Recommendation: Aircraft X told me they lost communication with Approach on 124.4 as they were descending through 8;000. 124.4 is a clearance delivery frequency for the TVY airport located 20 miles southwest of SLC with a large mountain between the two airports. I have no idea why Aircraft X was on that frequency but it appears Approach was either working several frequencies and wasn't aware Aircraft X was on that one or the Approach Controller thought that frequency had sufficient range. It is probably best practice to keep Clearance Delivery (CD) frequencies in a loud speaker if possible so you know if the aircraft is on a frequency intended for ground based communication; then take appropriate action.