Are serious issues with lag normally a problem with Android TV. I have a 2 year old sony bravia that can't stream video and change the volume at the same time. Even just changing the volume literally causes serious audio and video issues for the next 20 seconds or so. I don't want to buy a new TV so I was wondering if this is an issue if i were to buy an Android TV box or something.
It depends. On cheap smart TVs you'll almost certainly see lag when scrolling through menus, but nothing as bad as you've described. For Android TV boxes like the Shield, there's generally not lag.
Optimise you Sony TV:
https://www.tomsguide.com/us/sony-tv-settings-guide,review-5605.html
The nasty resource hogging Sony spy App is Samba, disable that shit in Android Apps settings.
Have you done a factory reset and debloat? If not an option or still have the same issue, buy a shield and just use the tv as a monitor
No that's not normal... My XD93 Bravia has no such issues. It's not far, but it really shouldn't lag when playing things or changing volume.