For US operators, AC 90-108 says:
NOTE: Approved RNAV systems using DME/DME/IRU, without GPS or WAAS position input, may only be used as a substitute means of navigation when specifically authorized by a Notice to Airmen (NOTAM) or other FAA guidance for a specific procedure. The NOTAM or other FAA guidance authorizing the use of DME/DME/IRU systems will also identify any required DME facilities based on an FAA assessment of the DME navigation infrastructure.
NOTE: Specific approval is required for operators operating under 14 CFR parts 91 subpart K (part 91K), 121, 125, 129, and 135.
. . .
8. USES OF SUITABLE RNAV SYSTEMS NOT ALLOWED BY THIS AC. An otherwise suitable RNAV system cannot be used for the following:
. . .
b. Substitution on a Final Approach Segment. Substitution for the NAVAID (for example, a VOR or NDB) providing lateral guidance for the final approach segment.
c. Lateral Navigation on LOC-Based Courses. Lateral navigation on LOC-based courses (including LOC back-course guidance) without reference to raw LOC data.
So, look at your OpSpecs and any applicable NOTAMs if you do not have GNSS.