It's good that the tarp is resting on stakes rather than the tree itself, but it would probably need to be completely sealed from the outside air in order to provide much protection from the cold. Tree lilacs are quite hardy so your tree should easily recover from any freeze damage to the foliage. We saw minor foliage injury on some of our tree lilacs last April 22 after lows in the mid 20s but there was no noticeable long term damage.

Lilacs are , syringa vulgaris, one of the hardiest plants out there. It should shrug that off no problemo

Yeah, lilacs are quite resistant to freeze damage. They pretty much always bud before the last freeze & incur no damage.

Agree with L Clark and beng that the new foliage on common lilac (S. vulgaris) is very frost/freeze resistant. Tree lilac (S. reticulata & S. pekinensis) foliage can also handle some frost, but probably not to the degree of common lilac. Potential damage also depends on how far the new growth has expanded. Photos of a couple of our tree lilacs after last April's freeze (4/22/21) - second tree was only in the ground about a year. .Both trees looked fine later in the season.

arbordave, I agree a very late freeze (late Apr/May) will wilt some lilac leaves, but never seen leaves outright killed. Same freeze can and has killed every bit of new growth on some of my other plants.