Have you tried buffalo/bison? That's low-fat and supposed to be more healthful than beef as to the fats is does have.
As far as low-fat beef burgers go, I guess you just want to buy 90% or 93% lean ground beef, or ground sirloin if buying it that way. None of that makes a very good hamburger, though; you really need to start with a fair amount of fat for that.
I agree with the second point., and I would be strongly against half-assing it with a pure hamburger. If you want it done right, you need fat in the meat. Buffalo is also a very lean meat, and while bison burgers are better for you than moo burgers, and perfectly edible, I still find myself wishing I was eating an actual burger when I eat one.
So instead, what I would recommend is lamb-burgers. I unfortunately don't have the exact recipe, but I really enjoy these lamb burgers my parents make, and they would be relatively low-fat and relatively nutritious. When I eat these, I don't think about how much better a normal burger would be, I just think about how much I enjoy these bad boys:
The basic lamb mixture is a combination of lamb, a really generous amount of spinach, garlic, lemon juice, salt, pepper and oregano, as far as I recall, for a greek taste. When this stuff is all mixed together into patties, I would say you can visibly see about 30-40% of the patties are green from the spinach, to get an idea how much spinach I'm talking about. Grill them like you would normal burgers. The only really unhealthy thing about the burger (not that I mind) is that it is served with a feta aioli, but if you use the feta sparingly and perhaps a light mayonnaise, it shouldn't be that bad. Top it with spinach leaves and red onion on a multigrain bun, and you have a pretty healthy burger, at least as far as burgers go, and I absolutely love them.
Another option would possibly be a Portobello mushroom burger? I enjoy these well enough. Like I said, I'd rather change up the burger option with unique variants than try to start substituting things and hope to get something close to the real thing.