Yes. Americans (and Canadians!) can get their visas for Lebanon at the border.
I met several (at least 5!) Americans while in Lebanon recently and they all got their visas at the border. One couple had trouble, though... when they left Syria, the Syrian officials failed to stamp them OUT of the country. They had to return to the border, get the exit stamp, then return to Lebanon. Otherwise, no trouble from what I've seen.
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