  We show that there cannot be more than 64 lines on a quartic surface
admitting isolated rational double points over an algebraically closed field of
characteristic $p \neq 2,\,3$, thus extending Segre--Rams--Sch\"utt theorem.
Our proof offers a deeper insight into the triangle-free case and takes
advantage of a special configuration of lines, thereby avoiding the technique
of the flecnodal divisor. We provide several examples of non-smooth K3 quartic
surfaces with many lines.
