They'd go for the Black Cherry, I'd think. But offer all and see which they choose.
Lilac is a favored nectar source, but I've never heard of any swallowtail using it as a host.

Thanks for the info I have always wanted to raise EST but could never find cats. I found six EBS on my dill and I have a second instar and a fourth instar are they from the same mother?

Typically they are not even in flight when my lilacs are blooming here in Southern Ohio. In this area, their favorites are Tulip tree, Black Cherry, and ash. Black Cherry is useful because so many things use it as a host.
Good luck,
Elisabeth