  We introduce an algorithm which combinatorially computes the
Castelnuovo-Mumford regularity of 321-avoiding Kazhdan-Lusztig varieties using
excited diagrams. This extends earlier work of Rajchgot, Weigandt, and the
author (2022) which computes the regularity of Grassmannian Kazhdan-Lusztig
varieties. Our results specialize to compute the regularity of all two-sided
mixed ladder determinantal varieties in terms of lattice paths.
