Majesty Palm seems to be a fickle plant. Granted, im still working on improving my green thumb, but I've struggled with both of the Majesty Palms I've had. The one I currently have has been outside for about 3 weeks (?) now that the weather is reliably warm both day and night here I SE Michigan. It is browning a bit though. It has been humid and mostly rainy here, but we did have a dry spell last week, so that might have done it.
To answer your question about indoor lighting, I had my Majesty Palm indoors the end of winter and a large part of spring and I misted the leaves regularly and watered occasionally. The grow light I used seemed to work well and extended the daylight hours for my plant. Here is what I used:
https://www.amazon.com/dp/B00PB94PCO/ I like it because it has a flexible head so I can point it in various directions and it has multiple dim settings, so I gradually dimmed the light some evenings (when I thought of it) for a more natural lighting effect for my plants. I recommend it. Like I said, though, my Majesty Palm is currently outside in the sun because I feel that's better for it during warmer months and I'll spray it down well with soapy water (to get rid of most of the bugs) before I bring it inside this fall.
I hope that helps!