The relationship between leaves and plants is equivalent to that between lungs and animals.

Literal

Leaves [and-と] plants [with-との] relationship [topic-は] lungs [and-と] animals [with-との] relationship [to-に] equal is-[である].

Variant with a slightly different structure: との instead of に対する, and 等しい ('equal') instead of 同じ ('same'). Note との: と (with) + の (attributive) = 'between X and Y.' 等しい takes に for the thing being equated.