'western-looking' is a Modern English compound formed from 'western' + '-looking', where 'western' derives from Old English 'westerne' (from 'west') and '-looking' comes from the verb 'look' plus the present-participle/adjective-forming suffix '-ing' meaning 'appearing'.

'western' developed from Old English 'westerne' (related to 'west', from Proto-Germanic *westrą). 'Look' comes from Old English 'locian'/'lōcian' (to look), and the pattern of forming adjectives with '-ing' (as in 'good-looking') in Modern English produced compounds like 'western-looking'.

Originally the elements meant 'west' + 'appearing', and over time the compound came to mean more generally 'having a Western style or appearance'.