As the very concept of dieting involves restricting your food intake in some manner, it is beneficial for anyone on ANY diet to take a good, balanced multi-vitamin.
However, for those on a low carbohydrate diet, it is even more important.
Proteins convert to energy more slowly than carbohydrates. This is why many people on high-protein, low carb diets report a lack of energy.
A good multi-vitamin gives you a boost from the balanced B-vitamins, which are also essential in the manufacture of red blood cells and the processing of amino acids.
Low-carbers may also be cutting their calcium intake to an unhealthy level, and a good multi-vitamin will help with this as well.
In addition to the purely physical importance, there is a psychological aspect involved as well. Dieters are more likely to “fall off the wagon” when they do not feel well, physically or mentally.
Taking a multi-vitamin is a good way to buy a little insurance against the lethargy, viruses, and “general blahs” that can hit if you allow your immune system to become depressed.
It is also a visible, repeated action that reminds you that you truly WANT to be healthy.