I would say buying their oil has more of an influence, rather than owning a .ly domain. The earning for the domains are probably insignificant compared to the oil.
Use less oil? I don't know how much oil comes from Libya, but you might be able to deny them more money by using less oil than not using a .ly domain (which is only a couple of dollars a year).
This should be upvoted far more than it is, because it is completely correct. Oil is a global commodity with a standard price; if you don't buy oil from Libya, you'll buy it from someone else for same price, and someone else will buy it from Libya at that price anyway; boycotting oil from them accomplishes nothing.
.ly domains do not work the same way. If you don't pay X$/yr for that domain, it's highly unlikely that someone else will buy it for the same price, since you probably tailored the domain to your business--so you are directly funding the regime with that money in a way oil is not.
edit: okay good, the parent was at 1 karma when I posted this and I was annoyed.
"it's highly unlikely that someone else will buy it for the same price, since you probably tailored the domain to your business"
I am not sure I agree with it. It seems against the notion that multiple people are working on your business idea at a given time. If bit.ly decided to not buy this domain, do you think it is unlikely someone else would not buy it by now regardless of existence of url shortener?
It's possible bit.ly would be bought up by now, but most less common ones I don't think would be. Poking around the internet, it looks like a .ly domain is at least $75 annually, which is a lot of money to just domain-squat on (especially since there are probably a many fewer accidental visits to .ly domains than to .com ones.) There doesn't even appear to be squatting on many variants of bit.ly (tried bti.ly, bot.ly, bpt.ly).