I've found this ILS-Y 26 EPBY approach, where there are two LOC minimums: With D3.0 and w/o D3.0 on Jeppesen chart. On the original AIP charts it says "When stepdown fix not received", but how could we possibly not receive the stepdown fix on LOC (only) approach, if DME is required? Both stepdown fix as well as recommended altitudes table are based on BYD, and there's no reference to BYZ on the final approach?
DME is required equipment for the approach procedure, but note that the LOC DME minimums only apply to the Localizer DME functioning. The missed approach holding pattern references the VORTAC DME, and not the Localizer DME. If the Localizer DME is out you cannot identify the LOC step down fix on the FA segment, but this does not mean the approach is not flyable. The MAP can be identified by using a constant groundspeed and clock method but this method will require increased minimums for (I presume) reasons of safety.
The approach is an ILS or LOC procedure, which means you are able to fly it if you are receiving the localizer and the glideslope (ILS) or if you are receiving the localizer only (LOC). A localizer does not have DME capability, so there are minimums published if you cannot identify I-BYD D3.0. (ILS DME information comes from the glideslope's location, generally speaking, but it is separate from the glideslope guidance—so it may still be working even if the glideslope is out, or it may not be.)
The procedure requires DME in general because the missed approach has you flying to the point BY633 before turning around and holding at BYZ VOR. The point BY633 is identified as the BYZ 255 radial at 4.7 DME. You need DME to identify it.