What's about the background? It is not, it's about the black edge. The background can make two things. It can highlight your subject or it can ruin your photo (this applies to portraits with backgrounds of course).
Camut - I didn't say the background is unimportant with portraiture. I was pointing out the fundamental issue behind the lack of impact in this second self-portrait, and that the light is the biggest factor. Granted the background isn't a good choice either, but for me the lighting here is all wrong so even with a good background, it's still not going in the right direction.
Alex, by oblique, yes, it means at an angle. Try 45 degrees as a starting point and review your image from that and then decide whether you need more or less light. Then you can fine-tune and change the angle for a recomposition.
Equipment can be a limiting factor in certain environments, but there are ways of knowing how to maximise what you have. The sodium lamp might be overkill without an umbrella or softbox. It could help but if it's shone direct at the subject, expect blown highlights without diffusion.