Yes, I have an iPhone 4. I know it's old and that's why iOS7 maybe lags on it so terribly, BUT if the was to slow to run iOS7 on it, why did apple mandatory released 7 for it? They want to torture their customers so that they switch to a new overpriced 5s?
To remove the keyboard lag go to Settings -> iCloud -> and turn OFF the Documents and Data. Reboot.