She lives on milk and vegetables alone.

Literal

[topic-は] milk and vegetables [only-だけ] [with-で] is-living.

生活する ('live, lead a life') here describes a sustained dietary pattern — Japanese uses 生活する for the broader 'live one's life' rather than the bare 'be alive,' which is 生きる. The instrumental で marks the means by which she's living — 'on (the diet of)' milk and vegetables. だけ ('only, just') restricts to those two foods. The pattern AとBだけで生活する is the standard 'live on just X and Y' frame — adaptable to medical situations (病院食だけで...), monastic asceticism, or extreme diets.