Diet and particularly exercise are effective, but keep in mind that when you're depressed it can be very hard to find the energy or motivation to cook, eat healthy meals, or exercise. Medication is useful even if it just gets you far enough to be able to do those.

Sleep is way more complicated. Insomnia predicts depression, yes, but they're also pathophysiologically linked in ways we don't quite understand. It's a symptom of depression as well as a cause. Sleep architecture changes are known, there are circadian factors, full-night sleep deprivation has a very powerful antidepressant effect until you sleep again, the list goes on. (Don't have any citations at the moment, sorry.) Of course not sleeping won't help matters, but treating depression like pure insomnia doesn't work very well.