Why the hell is Lebanon inserting itself into Libyan politics? The reason is very simple, as my business law professor at University taught me, we should always "follow the money".
The country of Libya for many years prior to 2011, had no international banks because Ghadafi knew better than to trust the international banksters. So, when a Libyan individual wanted to invest in business outside Libya, they had to establish accounts in foreign banks. For many years the Libyans and other Arabs and African's liked Lebanon.