Hi
What is the birth weight and current weight of the baby ?
I feel there are some feeding or latching issues. If baby is satisfied on hunger with a feed and burped properly, baby should sleep at least 2 hours after feed.
What you are saying are hunger cues that baby is trying to show. If baby is hungry or not burped properly, he / she wont sleep. It's not related to being on your lap or not.
Next Steps
take an online consult to discuss above and try to rectify lactation associated issues
Health Tips
weight gain has to be checked early on to prevent malnutrition in the long run
swaddling isnt the most ideal thing to do for a baby, if possible, let the baby be free if baby scratches face, use mittens for few weeks and then let hands be free