'Is' is grammatically correct, but you have set up a notional dilemma, and it would be cleaner to recast (and notice the spelling of 'vegetarian'): One of the most common types of vegetarian is the lacto-vegetarian. However, I don't think that there are more than 3 or 4 kinds of vegetarians altogether, so I find 'one of the most common' rather unbelievable. Lacto-vegetarians are either the most common or they are not.
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