  Inner amenability is a bridge between amenability of an object and
amenability of its operator algebras. It is an open problem of
Ananantharman-Delaroche to decide whether all \'etale groupoids are inner
amenable. Approximate lattices and their dynamics have recently attracted
increased attention and have been studied using groupoid methods. In this note,
we prove that groupoids associated with approximate lattices in second
countable locally compact groups are inner amenable. In fact we show that this
result holds more generally for point sets of finite local complexity in such
groups.
