There are two likely reasons that your new lilacs are drooping and they are opposites of each other.
Lilacs like to receive adequate water but don’t like to have their roots submerged. In Sussex County, DE the spring months have been very wet as you know. Some areas of the county have a layer of clay under the top, sometimes sandy soil. This keeps the water from seeping down into the ground and the result is that the roots sit in a bowl of water. I use a posthole digger in my yard in the Rehoboth area to prepare a spot for the plants by digging down through the clay layer which can be from less than a foot or so below the soil line to even deeper. Once the hole is deep enough that water does not stand in the hole fill the bottom of the hole with sand and then the top layer with top soil around the plant then mulch on the top.
Another very possible reason is just the opposite-not enough water. After the wet period that we had earlier we have had a recent period of much less rain sometimes with high winds for days. The fact that the leaves seem to be all pointed in one direction seems to be due to the wind. If this is a west or south facing area the drying effect would be increased. These factors tend to dry out the plants especially new plants which have not had a chance to develop a good root system. From the picture it looks like your top soil is sandy and would not hold water long (unless the clay problem exists). The fix here of course is to make sure the plant gets adequate water, one to two inches per week or more if the soil is sandy.
Checking the soil to determine if there is standing water under the plant or only dry sand or soil would be the first step in determining which path to take.
There are other possible causes that are disease related but unless your newly purchased plants were already infected, which is unlikely, these are probably not the causes.
The link below is a good reference for this problem.