Budrinna's answer is correct - I was in Tripoli last week (and in several other cities), and the new domestic terminal at Tripoli airport is a delight. It is fully up to the same standard you would expect from a domestic air terminal in Europe.
There are now quite a few private carriers operating domestic flights in Libya, in addition to Libyan Airways, the state carrier. Certainly there would be no problem finding flights on a daily basis to and from major cities.
One of the carriers (I can't recall the name, starts with a B) is using relatively late model DHC-8 (Dash-8) aircraft. One outfit has a DC-9 that is leased from South Africa. All in all, it's becoming a lot like Europe so far as low-cost domestic air travel is concerned.