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From the given name Luke.

From Middle English luk, lukke, from Middle Dutch luc, geluc, gelucke (“good luck, fortune”) or Middle Low German lücke, gelücke (“lot, fortune, fate, luck”), of obscure origin; perhaps ultimately related to German Lücke (“gap, opening”) in the sense of "space or opportunity", hence "chance". Cognate with West Frisian gelok (“luck”), Saterland Frisian Gluk (“luck”), Dutch luk, geluk (“luck, happiness”), Dutch Low Saxon luk (“luck”), German Low German and German Glück (“luck, good fortune, happiness”), Danish and Norwegian Bokmål lykke (“luck, happiness”), Norwegian Nynorsk lukke (“luck, happiness”), Swedish lycka (“luck, happiness”), Icelandic lukka (“happiness”). According to the OED, it may be related to lock. A loanword into English in the 15th century (probably as a gambling term), Middle Dutch luc, gelucke has parallels with Middle High German lücke, gelücke ("luck, skill, chance, profession, livelihood"; whence Modern German Glück). The word occurs only from the 12th century, apparently first in Rhine Frankish. Perhaps from a Frankish *galukki, derived from Proto-Germanic *lukjǭ (“opening”). The word enters standard Middle High German during the 13th century, and spreads to English and Scandinavian in the Late Middle Ages. Its origin seems to have been regional or dialectal, and there were competing German words such as gevelle or schick, or the Latinate fortūne from Latin fortūna. Its etymology is unknown, although there are numerous proposals as to its derivations from a number of roots. Use as a verb in American English is late (1940s), but there was a Middle English verb lukken (“to chance, to happen by good fortune”) in the 15th century.

From Middle English luk, lukke, from Middle Dutch luc, geluc, gelucke (“good luck, fortune”) or Middle Low German lücke, gelücke (“lot, fortune, fate, luck”), of obscure origin; perhaps ultimately related to German Lücke (“gap, opening”) in the sense of "space or opportunity", hence "chance". Cognate with West Frisian gelok (“luck”), Saterland Frisian Gluk (“luck”), Dutch luk, geluk (“luck, happiness”), Dutch Low Saxon luk (“luck”), German Low German and German Glück (“luck, good fortune, happiness”), Danish and Norwegian Bokmål lykke (“luck, happiness”), Norwegian Nynorsk lukke (“luck, happiness”), Swedish lycka (“luck, happiness”), Icelandic lukka (“happiness”). According to the OED, it may be related to lock. A loanword into English in the 15th century (probably as a gambling term), Middle Dutch luc, gelucke has parallels with Middle High German lücke, gelücke ("luck, skill, chance, profession, livelihood"; whence Modern German Glück). The word occurs only from the 12th century, apparently first in Rhine Frankish. Perhaps from a Frankish *galukki, derived from Proto-Germanic *lukjǭ (“opening”). The word enters standard Middle High German during the 13th century, and spreads to English and Scandinavian in the Late Middle Ages. Its origin seems to have been regional or dialectal, and there were competing German words such as gevelle or schick, or the Latinate fortūne from Latin fortūna. Its etymology is unknown, although there are numerous proposals as to its derivations from a number of roots. Use as a verb in American English is late (1940s), but there was a Middle English verb lukken (“to chance, to happen by good fortune”) in the 15th century.