The cache takes a while to rebuild itself during which time it's normal to experience lag.
I suggest playing with the Steam client which pre-downloads a good chunk of the cache.
Thank you for the answer. The lag issue started even while the cache was loaded, and it's happening on OSRS/RS3 as well. So I doubt the lag has anything to do with the cache.
Have you tried Razer Cortex? That program might help to disable a few things you're running that use the internet and it'd put your PC on High Performance while you play.
If that doesn't help, it's definitely a connection issue and I'd try either playing on a world that's hosted on a different geographical location or using a VPN. Even if the ping is higher, your connection might be more stable.