The question is why a website should use litecoin instead of bitcoin !?

Who says it has to be Litecoin instead of Bitcoin? Why not both? Why not Zoidberg?

ok, both. then the question is, why an end-user should convert his USD to litecoin and spend it instead of bitcoin ?!

Why convert at all if you have USD? Tongue

Just buy it with USD. If it ONLY accepts crypto, well then that's a different story.