Green’s Dictionary of Slang

lose out (on) v.

[note Asbury Sucker’s Progress (1938) 16: An extraordinary number of the terms, technical and otherwise, which were employed by Faro players in the palmy days of the game have passed into the language [...] Here are some of them: [...] Losing out—Betting on a card which loses four times in one deal]
[mid-19C+]

1. to fail, to miss an opportunity.

2. (also lose out to) to be fooled, to be swindled.