Breastfeeding would be damn near impossible-at least for the first 3-6 months while co-parenting separate, because they need to eat every 2-4 hours and if breastfeeding-that requires mom. Period.
BUT-it is absolutely possible to co-parent while living separately if you aren't breastfeeding or after you finish breastfeeding.
Furthermore-there is nothing stopping a lover who lives separately from being there part time to care for the baby. Just not likely to be able to manage equal split if you are breastfeeding. Due to the feeding constraints.
Many courts give parents split time who divorce (and yes, this often happens before the birth of an already conceived child).
With under school age, it's common for them to do a 3 day/4 day split. Meaning, child lives with one parent 3 days one week, 4 days with the other parent, then the following week, 4 days with the first parent and 3 days with the other. This (in my experience as we did it by court order with my stepson) SUCKS if you don't get along.
But-if you get along well and live near each other-that wouldn't be so bad.
We lived separately for a year and a half with 4 kids who went back and forth whenever they wanted to. It was no big deal. We were dating, weren't able to function sharing a home at the time-but were definitely wanting to continue co-parenting and seeing each other.
It was really-not a big deal BECAUSE we worked together and got along. So for example, whoever's home the child was sleeping at, the other one went over to tuck them in at night (we were only 1/2 a mile apart).
Short answer=yes it can be done.
But it requires you to be very well connected in working together and possibly need to be creative.
"Love As Thou Wilt"