So I've recently watched "Crazy Ex Girlfriend" (which is set in SoCal), and I've noticed everyone there pronounced "Law" and "Lawyer" differently, which was really interesting. To my ears, their pronunciation of "Lawyer" has a darker, probably more rounded sound. I checked on youglish and some speakers didn't make the difference. I don't know if this is specific to the cot-caught merger or Californian accents. I did notice before that surrounding sounds affect the quality of vowels even with the merge, but it's the same consonants so I'm not sure what's happening here.
"Lawyer" sometimes (usually?) has the diphthong /ɔɪ/, as transcribed here: https://www.dictionary.com/browse/lawyer. This seems to be very widespread across many accents. In american accents, the difference is more noticeable in accents that have the cot-caught merger, because the diphthong still retains a "dark" quality, and 'law' is pronounced with /ɑ/.