I have connected up my lifestyle 135 system to foxtel and apple tv 4k. And the quelity has reduced dramatically. When they are connected without the bose system they are crystal clear.
Thank you for reaching out via the Bose Community. Welcome to the site.
The Lifestyle 135 III has a maximum video output of 1080p, so it might be a better idea to connect any 4K devices directly to the television, then use an optical connection from the TV to the Lifestyle console.
I hope this helps, please let me know how you get on!
Jeff G - Community Support