I'm still on IOS 9.0 and have toggled off just about every setting. I think one of two things below might have fixed my issue with the lagging and stuttering. It's been working all weekend great.
1) General: Reset: Reset all settings. Do this TWICE! Your phone will reboot after each time. This won't delete data, but will erase custom wallpaper and wifi passwords, etc.
2) Settings: General: Accessibility: Keyboard
Toggle the switch for “Show Lowercase Keys” to the OFF position
Exit out of Settings to immediately see the effect anywhere the keyboard can be summoned
Change you keyboard to all caps. If it's already on all caps, change to lowercase. Whatever setting it's currently on, CHANGE IT to the other.
I now don't have issues.