Hmm...... thinking more about it, I actually need to retract my statement of "counter-intuitive to biologic evolution". Normally insects are guided to the center base of a flower, because that is normally where the sex organs are.
Duh! Not so with lilies!
Anthers and stigmas are usually well away from the petal surfaces. So it would make sense not to guide insects to the center base.
Unfortunately, I don't smell a lot of things that other people do, and detect things that other people don't. So I can't trust my nose. Basing my observations on insects, it's true, I do see them more often sipping nectar from the broad surface of petals rather than the center convergence point. But I've never seen them venture to the tips of petals, nor the edges. Most often I see them in the center third of the petals. Wondering though, what kind of differences there might be from species to species, and more obviously, from species group to group.