Intriguing, I never saw this kind of problem…
Could you check whether it's CPU bound, e.g. does Geany use a lot of CPU when the letters appear? Also, does e.g. scrolling in a file, or open one, show the same kind of lags? If so, maybe you could try and get a backtrace during the lag, by running Geany inside GDB and hitting <kbd>Ctrl+C</kbd> while it's lagging, and getting a backtrace there? it might need a few tries to get a meaningful backtrace, but it could potentially show where the slow code lies.
Also, could you post the debugging info from *Help → Debug Messages*?