Here is an explanation from English.stackexchange.com (fyi, here in the US, I have never heard “The Lebanon” but I do hear “The Sudan”): Professor Liberman says the habit of putting "the" in front of place names is heard throughout the English-speaking world and is common to Germanic and Romance languages. "In general, use of the definite article is unpredictable. Why should it be London but The Thames? There is no logic for it yet this is the way it is. "Sometimes country names go back to river names. As late as the mid-20th Century, everyone said The Congo because Congo is the river and named after the river, but no-one says it any more." He suspects that people once preferred to add the article if the place name related to a geographical feature like a group of islands (Bahamas) a river (Congo), a desert (Sudan) or mountain range (Lebanon). "Later the phrases were shortened, but the article survived. Hence the arbitrary rule that river names, the names of deserts and mountain ranges need 'the'.

No, no logical reason. It's a matter of custom & habit. I believe The Gambia and The Bahamas are the only countries that actually have "The" in their official titles. Other countries are/were frequently referred to with "the"s (e.g., the Netherlands, the Philippines), but it isn't technically correct. I don't think there's any way for you to guess or figure out whether a country gets an article. (As a side note, when I was younger, it was common to refer to "the Ukraine." "Ukraine" without an article is a change - https://books.google.com/ngrams/graph?content=in+Ukraine%2Cin+the+Ukraine&year_start=1961&year_end=2008&corpus=15&smoothing=3 )