if you have CL still means your baby is not yet full month and already taking 120ml 3 hrly!??! WAH!
anyway. my boy is 3 mths old now. he is on EBM. Initially i had supply problems, i still dont't have excess to stock up, so i am still working on pumping every 3-4 hours. But i know that after each latching on, then pumping will definitely help to 'empty' the breasts so that new supply will fill up and will increase overall supply.
There is not hard and fast rule as to how long to pump. For me, i pump left side 15 min, right side 15 min, then use hand expression coz pumping may not reach all parts. then another 5 min (left) and 5 min (right), and finish off by hand expression again. It's really tiring and tedious to do this every pumping session. I feed my boy every time he shows signs of hunger, which actually is pretty much 2.5-3 hrly, but he takes only 100ml per feed.