I too have a SAD lamp, and I also take Vitamin D3 supplements in rather large quantities. There is not enough sun in this country in the winter for our skin to manufacture Vitamin D, and as we get older we get less efficient at making it, too.
I'm not recommending any quantities, as I take far more than the Recommended Daily Allowance. I suggest you Google
Vitamin D3 + Depression, or something similar, and have a good read round before you make up your own mind.
If you have a sympathetic GP you might get a Vit D blood test done, but they're expensive so some practices don't do them.
Another cause of depression, lethargy, dry skin, thinning hair (and many other things) is an underactive thyroid. This can be associated with diabetes, and is worth checking for. Google
underactive thyroid + symptoms - very surprising! I've never had a blood test out of the normal range, but my GP listened to me and I'm now on 100mg of Levothyroxine. I feel a lot better for it
Best of luck!
Viv 8)