Dr Atkin's diet is not designed for bodybuilders. Caffeine is best considered as 'glycogen sparing' rather than a fatloss inhibitor. This is why endurance athletes AND bodybuilders like to use it pre workout. In both cases you need maximum glycogen burning. You do not lift weights to burn fat. Maybe I better emphasize that YOU DO NOT LIFT WEIGHTS TO BURN FAT. Heavy, intense (ie muscle building) exercise requires glycogen as fuel. It cannot use fat as fuel. So caffeine/coffee before an intense, anaerobic or endurance workout is a great idea. Keep in mind that caffeine loses its effectiveness if used habitually.
In any case it doesn't really matter if you burn fat while exercising, or just burn calories and raise your LBM/metabolism. As long as protein intake is adequate, you just need a caloric deficit to lose fat.