what color is the plant in natural light?

I think it's overwatered because the leaves on the bottom are soft/rotting, but you were right, it was etiolated due to lack of light (so the grow light would have helped it) but the over-watering is killing it.

The pot is kinda high for it, but not toooo bad. What kind of mix are you using? How often are you watering it? Echeverias are pretty hardy most of the time and can stand normal 50/50 perlite + normal cactus/succulent soil mix.

I think to save it, you have to do the usual behead, wait for stem to callous, and replant after roots start poking out routine. Or else the rot is going to spread.

good luck!

It's definitely overwatered and not getting enough light.

You can tell it isn't getting enough light because the spacing between the leaves - it's stretching in order to find some sunshine. This happened to my first echeveria that was grown indoors, too, even though it was right next to a sunny window. Echeverias love full, bright sun (I know that they say all succulents do - but in my experience that's not the case, as some are prone to scorching).

You can tell it's overwatered because the leaves are shriveled. Additionally, it looks like there are some calcium stains on the leaves. Are you getting the leaves wet when you water it? That's a big no-no for succulents. Always water the soil without getting the plant itself wet. Remember they're desert plants and aren't acclimated to being rained on, in any sense. Succulents are plants that do well if you neglect them by not watering them for long periods of time. They store water in their leaves, so they are more prone to root rot than other plants. Even in the summer in full sunshine, I only water my succulents every two weeks or so - when their soil is bone dry. They'd rather be dry than wet. If your succulent is not getting an ideal amount of light, then you should cut back watering even further because they won't be actively growing, and will be using less of the water in their soil. How often have you been watering? Indoors, I would water a succulent maybe once or a month or even less often depending on how long it takes for the soil to dry out completely. You really shouldn't worry about making sure it gets watered - I know I did when I first got succulents, but they honestly do much better if you just forget about them than if you fret over them. They don't like attention. I've found that soil type is not so important as long as you're watering it appropriately and the container can drain adequately. I've always used EB Stone Cactus Mix right out of the bag with good results, but like I've mentioned, I water very infrequently (but thoroughly when I do). I also see your plant is on a tray. It's very important, for all kinds of plants, not to allow them to sit in water. I take my plants outside to be watered so that the pots can drain thoroughly, and then I return the indoors ones to their trays. If you choose to water indoors, be sure that you drain any excess water off the tray.

As the previous responder pointed out, your best bet at this point would probably be to decapitate the plant and try to reroot it. The waterlogged leaves won't ever get any better once they look like that. You could remove them, but you'd have a lot of stem making for a very leggy plant. If you choose to propagate it (which is fairly simple, so I hear), I would even cut it above the bottom set of healthy leaves just because of the spacing - that will give the chance at a nice, tight rosette.

Additionally, I believe your light should be closer to the plant. I haven't used artificial lighting for my succulents before, but I've been told that the plant needs to be within a few inches of the light at the most to benefit from it.

Good luck!

Thanks so much all!