https://www.ifixit.com/Guide/Nintendo+Switch+Lite+Right+Joystick+Replacement/137374 Here's a comprehensive step by step guide with links to purchases the needed tools.
Fixing sticks on the switch lite requires quite a few more steps, the guy that broke his console doing it probably broke a ribbon or killed the usefulness of the thermal paste meaning the console will overheat much much easier. Just be careful, don't yank on anything too hard (unless it's prying the case open, that will require a decent amount of force) and keep track of which screw goes in which specific hole. A good tip for that last one is to have a large space and place the screws for each layer in their position in the space. Make sure to also use the correct screwdrivers listed otherwise you could round the screws and you'll have a worse time.
This is why the switch lite absolutely sucks. For comparason, here's the guide for fixing a normal right joycon:
https://www.ifixit.com/Guide/Right+Joy-Con+Joystick+Replacement/113185 A lot less work and a lot less risk. The way nintendo has layered things, its certainly like that stick is just under as much as possible.
I would reccomend following the guide though if you try it. Excersising your right to repair is a damn good thing and considering all joysticks have the same fault, there's a good chance it'll drift again even if you get it officially repaired. If you buy decent tools and learn how to do it now, in future (especially if you keep playing after the switch is not supported anymore) it'll be a very useful skill to have.
If you need help or advice on which specific tool kits to buy to save money on it, lemme know.