I'm losing weight right now, 42lbs in six months, so a steady, healthy weight loss. My diagnosis is severe recurrent depression, so I guess I qualify to respond to your question.

My answer is I'm doing exactly what convential medical advice tells me to do to lose weight, eating healthily and trying to incorporate a bit more exercise into my life. Depression doesn't stop me from doing either of those things and at the moment it is both helping and hindering me. Helping because I have lost my appetite and hindering because I am finding it hard to exercise regularly.

When recovering from depression in my 30s I gained an enormous amount of weight, that I've never been able to lose in a sustained way. I yo-yo, so for every 10 pounds I lose I regain 5, despite this I've lost more than 70lbs in total over the past 10 years. Right now, my weight loss "feels" different, my whole attitude to food seems to have changed and I don't get as many sugar cravings as I once did., I think that may be my medication which isn't a SSRI / SNRI or one of the older TCAs. Such antidepressants mostly have a reputation for inducing weight gain, though that wasn't always my experience.

I honestly don't know how I'm sustaining weight loss at the moment, my advice is exactly the same as it would be to anyone, ditch the faddy diets, eat less and do more, don't expect miracles and be patient.