I just got mine and it works perfectly. No noticeable input lag with a DS4.
I think I know why you were having issues. The bluetooth receiver in the adapter isn't very strong. I'm surprised they don't have it where it plugs into the USB port for power. If you've got too much 2.4ghz interference it'll cause issues or if you are out of a line of sight with the adapter.
I'll do some more experimenting. Recently I was unable to use it at all for some games as it wasn't being detected as a Dual Shock 2 (just a standard PSX pad) and they would refuse to start despite being fine previously.
There's no way I have too much 2.4GHz interference though as I live in a detached house right now and use ethernet for most of my consoles. I think the Wii U is the only device using 2.4Ghz wifi that's anywhere near my PS2. If it can't work in my use case then it can't for 99% of people.
Maybe I got a dud...