Not all adults can digest milk but most Europeans and people of European descent can. Most people of Chinese descent can't digest milk and East Asian vegetarians traditionally eat eggs. Vegetarians from India and surrounding countries typically drink yoghurt and eat processes milk products which works for them.
The Vegetarian Society recommends fortified soya, soya yoghurts, oat or rice milk, and vegan cheese.  Other milk alternatives aren't specificaly mentioned but most should be good. People eating a western diet without milk should ensure they get enough protein and calcium from other sources.
Milk and vegetarians
Before the 20th century Veganism wasn't possible because humans could only get vitamin B12 from animal products. Therefore every traditional vegetarian diet dating back to before the 20th century includes milk, eggs or both. Today veganism is possible since vitamin B12 can be got from bacterial fermentation. Milk is vegetarian since animals don't have to be killed to get milk but milk isn't vegan.