If carbs are keeping it high, not weight, then LCing WILL help. It can't hurt, especially if he does NOT do the lowest level of Induction. That could drop the BP too much when done along with the meds.

See if he will do a week eating more protein (good idea from that doctor) and salad and vegetables but NO SUGAR, STARCH or refined grains (= white bread). That would amount to Maintenance since weight loss is not his goal.

It's worth trying.