Be careful about the 90 days.
The tourist-visa is valid (in the country) for 30 days only - but it can be extended 2 times for 30 days each. This means that you can stay in LY for a total of 30 days. This regulation is not new...
45 days after you have stamped the visa in your passport at the LY-embassy of your country is correct as well. Also here be careful - this period can be different in different countries.
Another thing: If you enter TUNISIA - which is still normal if you want to go to LY - your car will be stamped in your passport. Once you leave TU for LY, you must take care, that the TU-customs DELETS this stamp. Otherwise, if you return after 90 days, you might have problems with TU since the TU-stamp is valid for 3 months as well. If the stamp is not deleted, they might think, that you bring the same car the second time...
Another stamp which is important is the so called "triangle-stamp" (police registration). This stamp you must get in LY within latest 7 days after your entry.
Best regards, Kuno