AFAIK, it's Dietes bicolor:
African Iris (Dietes bicolor)

It's at my Mom's house, in sun most of the day. It's always a mass of dead & live leaves, and only ever makes a couple flowers. It's been there for about 8 yrs. Does it need a more moist spot? Should it be mowed at some point annually? I'd move it for her if it could look better elsewhere. TIA!

for me? I would trim it up first, to get an idea how big it actually is under all that matted growth. cut it all the way back to about 3 inches tall, then dig it up and replant it in some good potting soil in a suitable sized pot and see what happens. now is a perfect time to do it. mix in some organic 5-5-5 slow release fertilizer into the top few inches of soil. post a pic if it starts to do anything!

TYVM! I think you have a great point about fertility, probably very lean soil. This plant was plunked in the lawn, after her dog dug a hole. I'm willing to move it, if we can figure out where it might be happier, but that's probably all anybody's going to do for it, besides maybe an annual trim. This plant doesn't do much for me, and Mom doesn't coddle anything (but grandkids.) :+) I've seen pics of them looking nice though...

if you're unsure about where to move it, might I suggest some place where it gets morning sun only. it may need more sun than that, but if you're sot sure then morning sun is a safe bet.

TYVM! That's my gut instinct too, a little less sun, more moist & fertile spot... I think this is the same flower I sometimes see in the ditch on the side of the highway. If so, I think that would mean it likes a much more moist spot than being in a sea of parched lawn.