  In this paper, we extend our result on a depth preserving property of the
local Langlands correspondence for quasi-split unitary groups
(arXiv:1804.10901) to non-quasi-split unitary groups by using the local theta
correspondence. The key ingredients are a depth preserving property of the
local theta correspondence proved by Pan and a description of the local theta
correspondence via the local Langlands correspondence established by
Gan--Ichino. To combine them, we compare splittings for metaplectic covers of
unitary groups constructed by Kudla with those constructed by Pan.
