I doubt your problem is coming from HDMI cable (esp. if it is less than 10m). Even a cheap cheap HDMI cable that comes along with blu-ray player will not cause noticeable screen noise and video lag. What is your TV settings right now? Screen noise when even watching blu-ray may be due to setting Sharpness too high (usually factory setting of Sharpness is too high). Have you ever use a calibration disc (e.g. DVE HD Basics) to perform the very basic basic adjustments on Brightness, Contrast, Sharpness, Color and Tint?
Zappiti Pro 4K HDR Media Player
Pioneer UDP-LX500
Pioneer SC-LX901
JVC DLA-N5
JL Audio E110
PS Audio Power Plant P10