I had the worst lag when typing after updating my phone, and I came across this website w/ instructions on how to fix it. Thought I would pass it along in case anyone else has this issue:
"You just open up the Settings app and navigate to iCloud > Documents & Data. That will open up another window where youll see a toggle switch. Turn it off if it already isnt (i.e., the circle in the toggle switch should be on the left side). After disabling Documents & Data, the keyboard should work just fine."
Here's a link to the full article as well:
http://www.gottabemobile.com/2013/09/19/fix-keyboard-lag-ios-7-iphone-4s/
"You just open up the Settings app and navigate to iCloud > Documents & Data. That will open up another window where youll see a toggle switch. Turn it off if it already isnt (i.e., the circle in the toggle switch should be on the left side). After disabling Documents & Data, the keyboard should work just fine."
Here's a link to the full article as well:
http://www.gottabemobile.com/2013/09/19/fix-keyboard-lag-ios-7-iphone-4s/