The world is screwed up because so many people jump into serious relationships they are not ready for and have children they are not capable of raising.
I would ask your bf to do a little self-analysis to discover why he keeps choosing non-maternal types, then having children with them. How selfish and cruel to the child! Frankly, you should get out before you hurt that child more by having him become attached to you, since you admit you can't give him what he needs so badly. Can't you persuade bf to let a loving grandmother/aunt raise him? You make it sound like the parents couldn't do a worse job if they tried.
Regarding leases...if you leave, the landlord generally has a legal duty to mitigate damages by finding another renter. They can't just sit back and charge you for the whole term of the lease without making a good faith effort to replace you. Perhaps under the best of circumstances, you might only be liable for a month or two that the apartment goes vacant. You also can look for replacement tenants yourself.
But please grow up before entering into an adult relationship again, especially when there are children involved; your rejection only served to make this poor child's self-esteem worse than his own parents have. Children can't raise children.