The lí reading is locked to the Korea family of words.
高丽 is the Goryeo dynasty (918–1392) that reunified the Korean peninsula and gave the modern English word 'Korea' (via Marco Polo's 'Cauli'). Modern Korea is
韩国 (South) or
朝鲜 (North);
高丽 is the historical and cultural label — used for traditional products (ginseng, rice paper) and historical references.