Not sure anyone is still paying attention to this thread, but...I've found it challenging. I'm no bodybuilder, but I am an Olympic lifter and amateur athlete (triathlons). What I've found is that being diabetic and eating low-carb has made gaining muscle far more difficult than it used to be for me. People above are right: protein helps to build muscle; carbs and fats can provide energy. The problem comes in the latter part of that equation.
In order for anyone to really build muscle you have to stress the muscles pretty well, eat sufficient protein, and get good sleep. While ketogenic diets work very well for some bodybuilders, others have tried and failed miserably. There are two reasons I can think of for this: some people have a difficult time having enough energy to really stress the muscles well on keto or similar; some people can't derive enough calories from a high fat diet to maintain weight at all.
I have both the first and second problems on keto: I tend to run too-low on glycogen to really push heavy weights; and I can eat 4,500 calories (nominally) on a high-fat diet and lose weight if I'm eating fewer than 50g of net carbs a day. I can get lean and maintain muscle mass (barely) by eating a high-calorie diet with sufficient protein and just enough carbs to restore glycogen. I only seem to be able to build muscle if I'm eating 100-125g of total carbs per day (usually in the 60-90g net range). However, the latter plan compromises my BG control. My solution has been annoying and simple: I've given up on building muscle and decided to train for triathlons
I'm doing my best to maintain my muscle mass (I'm still lifting), but have accepted that glycogen depletion and low-carb eating means my lifts are seriously compromised. Deadlifts and squats, for example, are about 50% of what they were two years ago (a year before my diagnosis). I eat just enough carbs to maintain (shooting for about 80-100g total; 50-60g net carbs per day), and rely on regular glycogen depletion from swimming, cycling, running, and lifting to keep my BG in check (works pretty well except on rest days, where I have to eat truly low carb).
Sorry, that's a wall of info. Short answer is simple: maybe. Some people can, some people find it difficult. I'm definitively in the latter category, after a lifetime of serious athletic training and an entire year (tomorrow is my "diaversary") of trying to train on various keto-like or low carb diets. Just doesn't work for me, but I've decided that BG management is far more important than strength or muscles, so I'm settling for becoming a lean, mean running machine.