  The aim of this paper is to study the Lipschitz normally embedded property
for a set and its medial axis. We consider if and when a non-LNE set implies
non-LNE medial axis and converse. We present an example a of Lipschitz normally
set that has medial axis which is not Lipschitz normally emebedded. At the end
we discuss special case when a set is a one dimensional germ on a plane.
