Due to the nature of USB, it either works or it doesn't - there is no extra latency from a long USB cable (technically 30 nanoseconds, but that's about 100,000 times shorter than you can notice).
Is the audio coming through HDMI too? Some TVs can have atrocious input lag, and if it's handling the audio too it could explain it. If it's the audio, you may have to run a 3.5mm cable along with the rest
If that fails, try and look at the lights on the converter - see if they're also lagging. It could be the controller isn't sensitive enough and only registers a hit some time after you actually make it. I think this is unlikely as even bad controllers register hits on time, you just have to hit them really hard.
Good luck!
Is the audio coming through HDMI too? Some TVs can have atrocious input lag, and if it's handling the audio too it could explain it. If it's the audio, you may have to run a 3.5mm cable along with the rest

If that fails, try and look at the lights on the converter - see if they're also lagging. It could be the controller isn't sensitive enough and only registers a hit some time after you actually make it. I think this is unlikely as even bad controllers register hits on time, you just have to hit them really hard.
Good luck!