There is a completely natural supplementation that a strict vegetarian like what you described above can take. It does not contain milk protein (caesin) and suitable for lactose intolerant individuals.
A good probiotic is not only a good supplement for the strict vegetarian, in fact, it might strengthen the immune system. It aids in the breakdown of food and its abosrption. Helps to maintain a healthy digestive system (GI tract) and prevent infection by harmful and pathogenic bacteria.
Lactic bacteria is classified by most govenment agencies as a food rather than a supplement as it should be live lactic bacteria and an organism. A good probiotic should have a sure bacteria count (revival rate), multi-strains including colonizing ones, and protected from the stong stomach acids when consumed.