I think i have a solution.
I had the same issue. I can confirm what you all have stated that it didn't happen with other apps, just with home and lock screens and that it went away once I slided or pressed the home button or opened an app.
Had a chat with Apple Support; they made me do a soft reset and they ran a remote diagnostic. Nothing showed up apparently. Support told me that this particular issue should have been resolved with iOS 9.0.2 update. So they suggested a full reset.
I did a backup, shut off "Find my iPad" on iCloud (dunno why they asked me to do it, but they were very specific about it); reseted the iPad as "new device" and updated to 9.0.2 from iTunes (I had previously updated from the device)... and it worked!
No problems with rotation anymore. No lag or slow-motion turns.
I will update this if anything happens. But so far, it worked.