Hi and welcome. That's a really pretty Dracaena. I'm probably not the best person to answer your question, but since nobody else has stepped up, I'll tell you what I know:
These plants grow here in Florida in regular (sandy, well draining) garden soil. Outside in the garden. It rains like crazy here in the summer and there is non-stop thick humidity from June through most of October. Is your plant growing in nothing but lava rock? They're not really desert plants. If you re-pot it into that nice IKEA pot in your picture, use regular potting mix, and mix the lava rock from the original pot into the new mix. That way it will drain well but at least hold a little moisture. Don't water it until the soil feels dry to your finger, at least an inch down in the pot. Yes! Stick your finger in the soil to tell when to water. It will depend upon how warm it is, how cool at night, and how humid it is (where are you, btw? ) as to how often to water, so you can't just say "I'm going to water this plant every Friday . . . " unless you have a perfectly uniform temperature and humidity.
They will do fine in some sun or shade here. I've never grown anything under lights except seedlings, but another guy on the Orchids forum uses those T5HO bulbs as supplemental lights in his greenhouses so it should give great light for your plant. But watch for signs of either a) leaves getting paler green means not enough light or b) leaves getting brown areas or edges means the light is too close to the leaves and they are burning. Oh, and don't forget this plant will grow taller, so . . well can you move the light up higher as the plant gets taller? Start out giving it no more than 3 or 4 hours/day of light. Is there NO other light source (window) near the plant? Natural light is much more gentle, not to mention gradual, than an artificial light turned on to Full On, then off again.
I wouldn't water it with your tap water if it is hard - usually this means it has a high pH and that can inhibit the plant from taking up some of the minerals in the plant food you use. Either distilled or the R/O water would be better. Rain water is the best if you can collect some. A balanced, soluble plant food once a month or so should be enough. These guys are not heavy feeders. Again, if it gets pale, increase the food a bit and the light duration.