I'm trying to regrow roots on this Haworthia I got from a big box store a few months ago. It was in a ceramic container with no drainage hole and it was in moss along with soil. Basically all it's roots were dead so I gently removed them along with some dried up leaves at the base. After about a week I used a small plastic cup, put a drainage hole in it, mixed aquarium gravel with cactus soil and put the plant in. It's spent time by a window and now it's under a grow light because I didn't think it was getting enough light. I water it about once a week using a dropper so I can put small amounts of water around it. It's late winter now where I live and temps are around 40s-high 50s outside during the day usually. The plant has some new root growth but there's also some dying leaves. I don't know if that's normal or if I'm doing something wrong? Any advice is really appreciated. This is my first haworthia.

Water until some comes out the bottom of the pot. The roots are below the plant so by using a dropper to put water around the plant, you aren't watering the roots.

Yes, water to saturation and then wait until the soil is dry at depth before watering again. The hole at the bottom should keep you safe from any potential harm due to watering deeply, as it will allow excess water to leave the container, but you can also check visually that this happened, given the container is translucent.

It's pretty much normal for the plant to look pretty sad while it is rootless, maybe a few lower leaves die back, so that would be expected. Up until the point when the new roots are able to take up some water and rehydrate the plant.

Your setup looks good and it should work great provided you have the grow lights dialed in (strength and duration). Expect the process to take weeks to months before there is a dramatic turnaround.

Okay I will water it more deeply. Thank you both for your input!