LO suck fist, sleep / no sleep, what’s should I do

Recently during the night/midnight, 3MO LO like to suck his fist sometimes he would continue sleep away, sometimes he is awake and couldn’t sleep back. I wan ask; 1. Should I carry him n lullaby him if he is awake and couldn’t sleep back, even after he cries for help or should I let him cont cry? 2. Sometimes It is also his feed time, but he din cry should I carry n feed him or just let it be unless he cries