Thanks for the info, Viceroy!
Hmm, I must investigate this...
Edit: Was it the SPEEDLINK SL-6603 Amiga Classix Diamond Edition + Competition Pro USB Joystick here
Customer reviews are favourable, e.g. "The controls are good and responsive", "The directional movement is very responsive" and "The main two buttons are also very responsive".
But if it was, then that's the same one I bought (and from the same place) and mine does
have the lag.
If the lag is gone from the one they're selling now, then it must be the long-awaited 3rd Edition!