Hi Hamtaro -
I'm new to this whole Lupus thing personally (only in the stages of diagnosis), but my aunty had had Lupus for quite a long time and has suffered from hairloss.
Obviously my advice needs to be consolidated with your doctor, but I have heard very good things about taking vitamin supplements that aid hair/nail/skin growth and health. My aunty takes the Swisse brand product for this issue, which contains ingredients such as Biotin ,Silicon, Zinc, Iron, Vitamin C and St Mary's Thistle. It's not a fast option but I've heard from her (and if you google this, many other lupus patients report it being beneficial) that overall it did assist hair growth.
She also uses a hair dressers product (not sure of the name) which comes in a small syrum type tube and she applies it daily - since using it her hair growth has actually been noticeable.
I hope you find a solution soon!