"Participants with low 25(OH)D levels (n = 230) at baseline were more depressed (P<0.05) than participants with high 25(OH)D levels (n = 114). In the intervention study no significant effect of high-dose vitamin D was found on depressive symptom scores when compared with placebo."

So it seems unlikely the cause is low vitamin D. Also, a sunlamp won't increase your vitamin D. More likely it is the normalizing effect of sunlight on the body clock.

Also, no supplement is going to increase serotonin levels in your brain. Your brain already has sufficient raw materials to generate as much serotonin as is required. That's just simplistic and wrong-headed nonsense, based on a lack of understanding about how the brain works.