Does plant protein really lack some essential amino acids? if so, wouldn't non-meat eaters die or become malnourished over time as a result?

NO,plenty of protein: No, it is not at all difficult to get all essential Amino Acids from plants. Combining legumes (beans, peas, peanuts) with either grains or nuts/seeds readily supplies all essential amino acids. See http://nutrition.About.Com/od/askyournutritionist/f/protein_combo.Htm the main nutrient that can't be obtained from a vegan diet is vit B12 so vegans should take B12 (but dairy ; eggs have b12).

No: Quinoa, a grain and soybeans are complete proteins. However vegans would lack the very important vitamin B12 and need to supplement.