1938, the word, like the thing, a forced mating of lion and tiger.
Entries linking to liger
lion n.
late 12c., from Old French lion "lion," also figuratively "hero" (12c.), from Latin leonem (nominative leo) "lion; the constellation Leo," from Greek leon (genitive leontos), a word from a non-Indo-European language, perhaps Semitic (compare Hebrew labhi "lion," plural lebaim; Egyptian labai, lawai "lioness"). Old English had the word straight from Latin as leo (Anglian lea).
The Latin word was borrowed throughout Germanic (compare Old Frisian lawa; Middle Dutch leuwe, Dutch leeuw; Old High German lewo, German Löwe); it is also found in most other European languages, often via Germanic (Old Church Slavonic livu, Polish lew, Czech lev, Old Irish leon, Welsh llew).
Extended 17c. to American big cats. Sometimes used ironically of other animals (for example Cotswold lion "sheep" (16c.; lyons of Cotteswold is from mid-15c.). In early 19c., to avoid advertising breaches of the game laws, hare, when served as food was listed as lion.
Paired alliteratively with lamb since late 14c. Used figuratively from c. 1200 in English of lion-like persons, in an approving sense, "one who is fiercely brave," and a disapproving one, "tyrannical leader, greedy devourer." Lion-hearted is from 1708. Lion's share "the greatest portion" is attested from 1701. The image of the lion's mouth as a place of great danger is from c. 1200.
Lowse me, lauerd, ut of þe liunes muð. ["St. Margaret of Antioch," c. 1200]
tiger n.
Old English tigras (plural), also in part from Old French tigre "tiger" (mid-12c.), both from Latin tigris "tiger," from Greek tigris, possibly from an Iranian source akin to Old Persian tigra- "sharp, pointed," Avestan tighri- "arrow," in reference to its springing on its prey, "but no application of either word, or any derivative, to the tiger is known in Zend." [OED]. Of tiger-like persons from c. 1500. The meaning "shriek or howl at the end of a cheer" is recorded from 1845, American English, and is variously explained. Tiger's-eye "yellowish-brown quartz" is recorded from 1886.