Also, the lamp could be putting out UVA and not much UVB, so it could tan without producing much vitamin D.
For just the vitamin D, I'd get a "5.0" UVB lamp in a bare-bulb fixture, designed and sold for indoor avian and reptile pets. Aim at arms and hands, and away from the eyes. They're about $15 per bulb, and should be replaced every 6 months, as the UVB output degrades over time. Afterward, they work perfectly fine as compact fluorescents, behind glass or under lampshades, for several more months, albeit shaped inconveniently for some fixtures.
A "10.0" bulb is for desert-species pets. The UV output is too high for the overall lamp brightness, and may damage your eyesight, as human pupils don't constrict enough. I suppose you could wear sunglasses, but that seems counterproductive to just buying a lower-UV lamp.
I'm pretty sure the answer to that is that they do not.
I dabbled in light therapy and found the first lamp I tried [1] very effective. However I have also started receiving comments from my colleagues about my nice new facial tan, in the dead of winter. I freaked out because the lamp was in my field of view 30 minutes per day every day without any eye protection, and sent the lamp back to where I bought it. Subsequently I have tried three different LED-based lamps and they seem to have no effect. I have carefully measured the light output and placed myself at proper distance to get the requisite 10,000 lux in all cases. No dice.
Here's the kicker - that lamp [1] appears to be the one used in some of the light therapy research (that's why I got it). It is entirely possible that much of light-therapy research was contaminated by badly designed lamps. There is no FDA certification for any of this as far as I know.
[1] Carex Day-Light Classic Plus Bright Light Therapy Lamp. Supposedly UV-filtered.