The phrase to leave someone in the lurch means to desert someone in trouble.
FRENCH & GERMAN
The Middle-French masculine noun lourche was the name of a game, no longer known, supposed to have resembled backgammon, denoted by the onomatopoeic word tric-trac in Modern French. By wrong division, it has also been written l’ourche — l’ is the definite article le (= the) before a vowel.
In this game, lourche was also used as an adjective: rendre quelqu’un lourche (literally to make someone ‘lourche’) meant to cost someone the win.
More broadly, used as an adjective after the verbs être, se trouver and demeurer (= to be, to find oneself and to remain), lourche meant disappointed, discomfited, deceived, duped.
It is difficult to explain the connexion between the word lourche as the name of the game and its use as an adjective meaning discomfited.
It is possible however that the origin of the French adjective, as a gaming term, is dialectal German lurz or its derivative lurtsch, both meaning left, wrong (the left hand being emblematic of bad luck) and both used to designate a game; lurz werden (werden means to become) is or was a phrase used in various games to express the failure to achieve some object aimed at.
The German equivalent of to leave in the lurch is im Stich lassen — lassen means to leave, im means in, and Stich has the sense of score in card-playing.
From French, English lurch was also the name of this game, as is attested in A Dictionarie of the French and English Tongues (1611), by Randle Cotgrave:
Lourche. The game called Lurche; or, a Lurch in game.
Il demeura lourche. He was left in the lurch.
The word lurch was also used in various games to denote a certain concluding state of the score, in which one player is enormously ahead of the other. In particular, a lurch was a ‘maiden set’, or love-game, that is a game or set of games in which the loser scores nothing. This sense is first attested in A Worlde of Wordes, Or Most copious, and exact Dictionarie in Italian and English (1598), by John Florio:
Marcio, a lurch or a maiden set at any game.
And, at cribbage, lurch denotes a game in which the winner scores the full 61 before the loser has turned the corner of the board by scoring 31.
In the Oxford English Dictionary (2nd edition – 1989), the earliest attestation of the technical use of lurch (a score in which the winner is far ahead of the opponent) is the above-mentioned quotation from Florio’s dictionary, while the earliest example of the derived colloquialism to leave in the lurch dates from 1596. However, in a comedy titled Misogonus (circa 1566-77), lurch was already used technically in a manner which immediately foreshadows its employment colloquially to signify discomfiture, disadvantage, etc.:
I’ll play still, come out what will, I’ll never give over i’ th’ lurch.
The word lurch meant discomfiture in general in the following phrases:
– to give someone the lurch: to discomfit, get the better of, someone
– to have, or take, someone on (or in, or at) the lurch: to have, or take, someone at a disadvantage
– in someone’s lurch: in someone’s power
– to leave someone in the lurch: to leave someone in adverse circumstances without assistance.
Only this last phrase is still in usage nowadays. About it, the British philologist Ernest Weekley (1865-1954) wrote, in An etymological dictionary of Modern English (London, 1921), that two words might have amalgamated: the synonymous phrase to leave someone in the lash, copiously recorded some years earlier than to leave in the lurch, suggests some connexion with the French verb lâcher, to let go, as in Modern French lâcher un ami, to leave a friend in the lurch.