Hello! I want to speedrun this game, but I only have it on a Lite, any recommendations on how to hook it up to my PC without a Dock?

If you don't have a dock, then I don't think there's a way to hook up the Switch on to your PC.

The only way to capture footage from a switch lite in something like OBS is with homebrew I think and you need to hard-mod the switch for that... I think I have seen people submit runs with a camera pointed at the screen, so that is an option if you want to run the game with a switch lite.