LyX is generally pretty good, but sometimes things that should be simple can be a pain. I couldn’t successfully get long URLs to wrap over multiple lines rather than overflowing off the edge of the page until I read this obscure bug report after about 5 minutes of Googling.
What worked for me was using Insert->URL instead of Insert->Hyperlink. Simple as that, I didn’t even notice there were two different options previously.
As a bonus you can make URLs clickable in PDFs by going to Document->Settings->PDF Properties->Use Hyperref Support.