To travel to Libya you need a visa, only Arab and certain African countries nationals are exempt from this requirement. Visas can be issued for several reasons, Tourist and Business are the main reasons. Due to the growth of the Libyan tourism industry, visa rules have been relaxed and are easier to obtain.
The visa application has to go to the Ministry of Interior & if you have evidence of visiting Israel in your passport you may not get a visa.
Process takes at least a week.
Libya visa information
Libya embassies
Foreign embassies in Libya