Lebanon is not part of the US, so the only ones voting there would be US citizens living there otherwise Republicans or Democrats abroad. On election day, their votes will be counted in the last state they lived in. Its not like France or Italy where they have electoral districts globally for abroad residents. Off course the US lets those abroad vote unlike some, for example where I live in Canada, if you are Canadian who has not resided in the country in the past five years you cannot vote. I am not sure how many other countries follow this although it is a rule I generally support, mind you unlike the US we don't tax citizens living outside the country either.
Of course Lebanon is part of the US. So is Syria. With Alaska and Hawaii they are the four states not part of the 48 contiguous states.
Nonsense. I don't recall the US invading either country or either country asking to join. Never mind I doubt the US would want a Muslim majority state, which both are. Hawaii and Alaska are different as they voluntarily joined the US.