I have iPad 2 and writing has become totally bad with it now. Something is hooking up the resources or it is getting old after 3 months. How can I make it faster?
Back up your iPad, then power it off.
Start the device and run only the problematic writing app. Get benchmarks or some other definite measurement so you can then try things and know if it helps.
You might also try the above while the device is in airplane mode to ensure no background sync or network issue is affecting the performance of the device and app.
The most common fix is to restore the device to factory settings and repeat the one app only. If that app works, then you'll need to restore the backup and work out what is causing the issue.
If that app doesn't work, then you can blame that build of that app and run an older one (again looking to get it from a backup) or find a different app.
The troubleshooting process is the same for most any problem.