You can get into Lebanon by plane and by boat.
Beirut International Airport sees a number of flights landing and taking off on a regular basis. Middle East Airlines provide services daily, to Abu Dhabi, Abidjan, Amman, Accra, Athens, Cologne, Cairo, Copenhagen, Dubai, Doha, Dammam, Frankfurt, Geneva, Istanbul-Ataturk, Jedah, Kuwait, Kano, Larnaca, Lagos, London-Heathrow, Milan-Malpensa, Nice, Paris-Charles de Gaulle, Riyadh, Rome-Fiumicino and Warsaw. If you are coming in from the UK, carriers such as Turkish Airlines, Czech Airlines and Air Serbia will serve you.
Between Tripoli, Lebanon and Tasucu, Turkey there is a seasonal ferry running weekly that serves a lot of people. However, currently, travelling by boat is not recommended as many consider it to be dangerous.