The more stuff you grow in soil, as opposed to leaving it barren, the better the soil health becomes. This includes lowering summer soil temperature, improving soil structure and tilth, more of the beneficial soil organisms and greater porosity. But yes, there might be some root competition between the alliums and lilies, and your lilies might multiply less vigorously. (Or, the lilies might actually do better, because of the aforementioned.)
But what good is a fast growing lily if you never see the flowers because they get eaten by rabbits?
