Welcome!!!
Here's a question for you, when she's inside her enclosure, is she purposely staying out from under her lights there too? Like going into a hide/cave or trying to stay underneath something? The reason I'm asking is because their behavior outside of their tanks/enclosures is usually totally different than their behavior when they are inside their tanks where there is light available at all times. Only if they are continuously and purposely hiding from their lights while underneath them is there an indication of a problem/issue, like brumation or illness. The fact that he's finding spots to hide/sleep out in your room/house isn't really a good gauge of behavior...
That being said, 4 hours a day of UVB/UVA light and proper temps will certainly cause him to be lethargic, just the cold temperatures all day alone will cause him to be lethargic, and then coupled with a lack of UVB and UVA light I'm not surprised he slowing down when outside of his tank for that long...why do you have him out of his tank every day for so long? We always advise the time period that you should leave both their basking bulb and their UVB tube on every day for as being between 13-14 hours a day, assuming that they are out of their tanks for a few hours a day, that way they will still get adequate UVB and UVA every day, and they'll stay warm enough to properly digest the food that they eat and for their bodies to do the functions that they need to do.
Just keeping her that cold all day long is not good, she most likely is not properly digesting her food or absorbing/processing any nutrition (vitamins, minerals, etc.) simply because she's too cold all day. Average room temperature in our homes is what, between 70-80 degrees? And their Basking Spot Surface Temps are between 100-105, with a surrounding ambient temp between 88-93? So you can see the issue with only having her in proper temps and under UVB/UVA for 4 hours a day...
