I don’t know of the game not registering inputs (you can press [F3] to toggle debug info, showing you what keys it thinks you press and what movements are in the queue, plus some positions and distances), but I know it has a bug of sometimes not fully registering that you landed on a platform, making you glide and unable to jump (which can feel like a missed input). To mitigate that, you can zoom in a little or reduce the size of the game window, or try in a different browser and/or on a different screen or device if you have multiple.
I also know about the lag, that’s because I made the decision to render the game in the browser DOM, meaning the browser applies all of its logic to each and every visual element in the game as well.