There are beef dishes you can make that are low fat and don't require any salt to taste good. Naturally the best tasting cuts of beef have some fat, but if you use the right combination of marinades and seasonings, very lean beef can be tender and taste great.
The leanest cuts of beef are top round, tenderloin and sirloin. The last two don't require a lot of marinade to make them tender but they're more expensive than the top round which is basically thick muscle and you need to do something to it to make it edible. If you marinade a piece of top round overnight in something like red wine vinegar or lime/lemon juice, it breaks down the muscle fibers and makes it pretty tender. Get a couple forks and poke holes all through the meat so the marinade can get all the way in. Throw some extra light olive oil in the marinade (or something like Wishbone italian salad dressing) and it makes the meat a lot more juicy after it's cooked. Seasonings can be just about anything you like (except salt). Salsa is great in marinade, onions, garlic, it's all good. And remember when you grill meat the browning from the grill gives meat a salty taste without the salt, although I'll bet most doctors would probably think that's as bad or worse than salt. You can also make beef stew or vegetable beef soup with top round as long as you cube the meat and let it simmer for at least a couple hours.
Good luck!