Breastfeeding would be damn near impossible at least for the first 3-6 months while coparenting separately, because Baby needs to eat every 2-4 hours. If you are breastfeeding, Baby requires Mom. Period.
But it is absolutely possible to coparent 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. You're just not likely to be able to manage an equal split if you are breastfeeding, due to the feeding requirements.
Many courts give divorced parents split time. This often happens before the birth of an already-conceived child.
With under school-age kids, 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, it 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 functionally share a home at the time, but were definitely wanting to continue coparenting 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 parent went over to tuck them in at night, as 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 you'll need to be creative.