If the lilies you planted are the sort that have stem roots (feeder roots that are near the surface) then gently removing any Zinnia seedlings that sprout too close to the stems would be useful.

The Zinnias will, hopefully, provide shade to the ground and that will please the lilies (cool feet, warm tops).

It might look a little 'sparse' this year - yet there's room for the individual plants to develop clumps.

If it's looking too open you could always pot up some more lilies and sink the pots into the ground to give a better showing, with the option of raising the pots at the end of the season and planting elsewhere at a density that's more pleasing to you.

I think the young Zinnias will transplant if you lift them carefully, with plenty of damp soil around their roots.