Probably nothing will happen. Nameservers for .ly are
dns.lttnet.NET, dns1.lttnet.NET, ns-ly.ripe.NET, auth02.ns.uu.NET, phloem.uoregon.edu. Of these only dns.lttnet.net and dns1.lttnet.net are hosted in Libya. If the dictator will have the local internet shutdown, he probably will not go to the lengths of also clearing all foreign DNS caches listed above.
Nonetheless I would be more careful in selecting a ccTLD to base my business on. Read, for example, about Gaddafi's dealings with Switzerland and you know which laws Libya follows at the moment.
As of right now, dns and dns1.lttnet.net (in-country) are unreachable, but the out-of-country nameservers are responding with what I presume was their last zone transfer. bit.ly still works, for example, but because of the outage, nic.ly is dead.
Nonetheless I would be more careful in selecting a ccTLD to base my business on. Read, for example, about Gaddafi's dealings with Switzerland and you know which laws Libya follows at the moment.