Personally, I would add some data to your search engine every time a person makes a new search query by searching that same query on youtube's api (https://developers.google.com/youtube/v3/code_samples/) or by scraping the data. Now that you've got some relevant results, you can sort through those (or all of the URLs you have collected) to give a more refined list of search results. If you want to pay me to get it done, I would be fine with that too.
The problem with buying a premade list (even if there is such a thing) is that it would be a whole lot of trouble to keep it updated.
HTML is repetitive text, and that is what conventional compression algorithms (like the ones you mentioned) are good at. How they work is pretty interesting, so I'd encourage you to go look it up.
The fact that you need to compress HTML makes me think there is a bigger problem, though (People shouldn't make complicated web pages).