I noticed in this new Doom+Doom II release there are lines in the image but they aren't there when played through GZDoom. Does anyone know what's causing this or is it the kex engine? I attached an image and I drew some lines pointing out what I'm talking about. It looks even worse in motion.

Looks like you never played original DOOM on the original hardware. And GZDoom gave you wrong personal imprinting. Those "lines" always been there due to the nature of the software renderer with precalculated fade table. Sort of a graphical artifacts.
ZDoom family and GZDoom specifically have their rendering code rather different from the original, so resulting picture looks noticeably different. While Kex attempts to simulate original software fading and produce more authentic look.