My advice, if you're doing well on Atkins (you haven't specified if it's inducion or maint), then fine. Just start out training with a beginners program, see how you feel, if you get an energy dump, then up the carb a bit.
Now, after a while, a lot of lifters have turned to what they call a CKD or cyclical ketogenic diet if they prefer the low car thing. Vince Gironda was one of the first that I know of to use this with his rainees. For 4 days, he would have them on modhigh fat and protein, very low carbs. On the 5th day, he had them on mod protein and carb, low fat, then repeat. Today, along these lines , Dr Mauro DiPasquale (a former IPF world PL champion and a highly respected physician) has come up with the Anabolic diet, which is basically 5 days low carb, 2 days lower the fat, carb up. It has evolved into the Metabolic diet, which doesn't have the stringent guidelines the Anabolic diet does. Do a search on these two diets for more specific info. Both Gironda and DiPaquale have had good results both on themselves and with their trainees.