The documentation contains the following inverse for the 1D case:
dtft = ListFourierSequenceTransform[{1/5, 1/4, 1/3, 1/2, 1}, ω]
Table[InverseFourierSequenceTransform[dtft, ω, n], {n, 0, Length[dtft] - 1}]
In higher dimension
InverseListFourierSequenceTransform[L_, p_List] :=
Normal[SparseArray[With[{sz = Length[p]},
With[{xs = Unique[ConstantArray["x", sz]],
cs = Unique[ConstantArray["c", sz + 1]]}, (Remove /@ Join[cs, xs]; #)&[
(List @@ InverseFourierTransform[L, p, xs + 1, FourierParameters -> {1, 1}] /.
Pattern[Evaluate[Last[cs]], Blank[]] Times @@ MapThread[DiracDelta[# +
Pattern[#2, Blank[]]] &, {xs, Most[cs]}] -> #) &[Most[cs] -> Last[cs]]]]]]]
which also works in 1D if you provide the variable argument in a list.
Note that it is only a right inverse. A left inverse doesn't exist because of the we don't have injectivity:
ListFourierSequenceTransform[{1/5, 1/4, 1/3, 1/2, 1, 0}, ω] ===
ListFourierSequenceTransform[{1/5, 1/4, 1/3, 1/2, 1}, ω]
True