I think my answer to that comes in at least two parts -- at least one of which is "I don't know"
The Latin word locus was borrowed into early Welsh -- it's in the GPC under the form llog, and it occurs in the Computus fragment, where I think the Latin phrase locus vacuus 'empty space' is translated as llog gwag -- spelt loc uac in Old Welsh, IIRC, which explains why someone I used to know regarded Old Welsh as basically Latin with a few sound changes, no endings, and a really irregular spelling system
So Yes, locus would give you the ll_g root you're looking for -- but presumably it wouldn't give you the right vowel in-between. Why not? I honestly don't know -- I think that trying to find out would lead you down a wormhole full of phrases like 'ultimate i-affection', and possible comparisons to Gaulish, so for now I'm willing to take it on trust!
Well, I think it's only a mystery because (a) we expect names to mean something, like Cymry being something like 'companions' or 'comrades'; (b) we like to think that understanding it might tell us something about English-Welsh relations in ancient times, if not more recently; so (c) we're interested in it. I think there are actually loads of linguistic phenomena that are unexplained, that only rate 'puzzling' rather than 'mystery' because they're just not that interesting -- unless you're particularly geeky, or think you can string them out into especially nerdy clickbait One example might be those words (I can't think of any off the top of my head, unfortunately) that can be securely reconstructed for, say, common Celtic or Proto-Germanic, but not for any other Indo-European languages: we're often tempted to suppose that they come from whatever pre-Indo-European peoples the Celts or whoever must have met/conquered/married on their travels, but we generally have no way of knowing. Or another one would be so-called s-mobile, where you get words that have an s- on the front in some languages and not in others with no apparent pattern or reason: a couple of examples are Welsh tarw, Greek tauros, English 'steer'; or Welsh to, Greek stegos, English 'thatch'. (I always like to think of a Stegosaurus as a thatched lizard.)