Mac external display issues

My Mac (2013) has no issues, I'm still very happy with it.

However, working with Premiere Pro a lot, I've added an external monitor (LG E2442 Display) using a DVI connection, through to an adaptor which is feeding into the Mac's Mini DisplayPort/Thunderbolt. The result is clearly faulty somewhere as I'm left with horizontal green lines (especially over black background) and lagging motion. This can be viewed here;

External monitor issues - YouTube

Has anyone encountered this issue before? Or does anyone know anyways I could troubleshoot the issue?

Many thanks