You can do Atkins using high quality proteins, or try South Beach. I don't think there's any Atkins rule that you have to eat poorly. I don't think you'll have much success building or maintaining muscle on no carbs, but 40/40/20 is not carved in stone, either. I do best on 50P/25C/25F.
Another way to stay on a diet with your dad but have enough energy to lift would be to add a portion of a carb to your pre and post-workout meals. This is assuming that you do the 5-6 small meals a day thing. If not, I'd suggest adding a portion of oatmeal to whatever meal you eat before you lift, and then a post-workout recovery drink: protein powder and a fast acting carb, like fruit. If your dad isn't exercising, he doesn't need the extra calories or the carbs for lifting.
Another option: look into a plan called NHE (Natural Hormone Enhancement) or CKD (Cyclic Ketogenic Diet). They are both based on eating very low carb most of the time, with periodic "carb-ups" to replenish glycogen supplies in the muscles and liver. They tend to be very effective fat burning diets, but require that you jiggle your lifting scheme so that you do your heavy lifting right after the car-ups, then a gruesome, full body depletion workout before the carb-up. Both diets take some getting used too, and IMO are not terribly healthy in the long run, but you might be able to adapt them to something you and your father can both do. If you want more info and can't find it, PM me and I'll see what I can find. I did CKD briefly about a year ago and lost some weight, but hated the workouts. Also, the carb-ups were a real binge trigger for me.
Hope this helps,
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