You can. But it's hard work. Because eating vegetarian makes it a lot harder to get a full protein profile. But it's not impossible.
According to what I've read lately, the idea of "complete protein" being difficult to get on vegetarian diet is so over-exaggerated that it is practically a myth. The original text the idea appeared in has since been revised, the author wishing they could take it back, since it is the most often repeated drawback to vegetarian eating, preventing who knows how many people from making a lifestyle change that would actually be quite healthy.
The truth is, the body holds amino acids in reserve, and matches them later with the complimentary requirements to make complete proteins.. And if you're eating a variety of food, then you really don't need to worry about making a complete protein in every meal. Just eat a variety of vegetarian protein sources and don't worry about it.
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