Unless I'm mistaken, neither the Ring doorbell or camera (at least by necessity) uses any "outside the lan" resources unless you are connecting to them remotely.
If you're getting this issue with these two, and only when they are activated, the first thing I'd try is getting rid of a number of the devices that are connected to your lan, temporarily, and see if the lag persists with a significantly lighter load on the lan itself. If it does not persist then you have your answer (most likely) that the addition to the lan of those devices, given it's normal "working load," pushes the demands past its capacities.
If that's the case a new router might, not will, but might, solve your problem if you get one that has expanded throughput capabilities beyond what you currently have.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
Memory is a crazy woman that hoards rags and throws away food.
~ Austin O'Malley