Does anyone know how to get rid of these black lines? Is this normal?
No, but that sort of thing could be caused by running the core with increased internal resolution.
Yep. Make sure you configure the core to either use the native resolution of the emulated game, or in cores that have “downsampling” or “supersampling” make sure to enable that option when you set the internal resolution to something higher. For example in Swanstation, if you set the “Internal Resolution Scale” to something higher than 1x, then you should also enable the “Downscaling” option so the output gets downscaled to something that will work OK with CRT shaders.
CRT shaders in general only work correctly when they receive the native resolution of the emulated game. For N64 Zelda, that would be 240p.
I can’t use downspampling, though I did decrease the resolution to 640x480 and that seemed to have fixed it, thanks!