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高丽 is the historical and cultural label - used for traditional products (ginseng, rice paper) and historical references.