I’m genuinely interested: do you have any example of a GIF/LOL website which owns the rights on the published content?
You either have no money to pay for a lawyer and go bust or you buy all the lawyers so that no-one will be left to sue you... sort of kind of... doesn't make sense but you catch my drift right? :D
"But everyone else is doing it" is the kind of reasoning small children use.
I think the only solution to respect the copyright for this kind of content (amateur content with no identified author) would be to stop publishing it: you can’t sue Tumblr, Facebook, Twitter etc.
Just to be sure: are we talking about the original authors, or the websites who add their watermarks on it?