[Hugh]

Hi Richard ... you're correct. The missing stamp is almost certainly another of the same stamps. I assume it just fell off. 

The General Headquarters (GHQ) of the Middle East Forces (MEF) in 1943 was located in Cairo. Then, the question becomes, what was the postal rate for a single letter from Lebanon to Egypt on September 13, 1943 (i.e. the date in the Beruit CDS)?

That's a challenge and a half. Following Vichy / German Administration, a coup, and a British Invasion, Lebanon was under Free French and British Administration overseeing a rising group of nationalists who wanted independence. I found a reference to an official text dealing with wartime postal rates, Arrêté no 1 of the Haut-Commissariat, 15 Jan 1942. It is quoted in the appendix of William C. Robertson's Syria & Lebanon – Free French Censorship WW II 1941-45 (Civil Censorship Study Group, 2011, pp. 122-123). It reports that the rate was “10 piastres” for a 0-20 g letter to Egypt". 

Assuming the rate was 10p, it is, as you say, reasonable to conclude that the missing stamp has to be one with a value of 5p. Most likely a twin to the existing 5p stamp that is still on the cover.

If so, the answer to Q1 would be:

Republic of Lebanon, Under British / Free French Administration
Stone Bridge over the Dog River Gorge [Nair el-Kelb]
Issued in 1940
5p, Blue-green
Sc. 155

The Social Philately aspects of the cover are interesting too. The person who sent the cover, Bayard Dodge, was the president of the American University of Beirut (AUB) 1923-48. He was a celebrated Arabist and a champion of wartime relief.

My favorite part of the cover are the Free French Censorship marks.

The purple, single ring censor mark, with a Cross of Lorraine and C P 2 = Contrôle Postal [Postal Control]; the 2 is the number of the individual examiner / censor desk.
The other purple numbers on the front 17 and back 15 would appear to be workflow codes used at different steps in the process. The word English in the upper right of the front of the cover was also a censor requirement on all mail. The language of the letter needed to be identified to ensure that the item was referred to a censor who could read that language. 

Definitely a cool cover. 

Thanks for your information about the US auction. However, I don't collect US stamps and have very little interest in them.

To each their own. I don't do varieties or worry about grading or shades ... although I have lots of respect for people who do. My own interest is focused on stamps and covers as historic artifacts ... stamps on cover, the contents, the cancels, auxiliary markings, the rates, the routes, the social and other historical context.  

Cheers, Hugh