At the beginning of last week's The Blacklist episode, The Vehm, we see Liz writing out a pros and cons list for having (and keeping) her baby. As would be expected, the cons most certainly outweighed the pros. Reddington's name is near the top of this list, as he is one of her primary concerns, at one point even telling him, "you are the only reason I need protection." After discovering that he has moved her neighbor out of the adjacent apartment in order to have round the clock 'security' next door for her, Liz calls an adoption agency, closing the episode.
In this week's episode titled Alistair Pitt, Liz continues with the adoption process (ending this episode with an offer for a closed adoption), abstaining from telling either Red or Tom both of whom have or would have objected, and for good reasons.
It is understandable that Liz would want to give her child a normal life away from the dangers she faces on a daily basis, but Liz should listen to Red and Tom when it comes to the safety of her child. If she really thought the situation through, she would realize that her child, with anyone else, not only puts the child in more danger but also puts the adoptive parents in danger. If the Cabal is really still out there, and is still actively pursuing her, then that baby will be safest under Red’s, Tom’s and her own protection, as there is no doubt Cabal would be able to find her baby if they chose to put it up for adoption.
There is also no doubt that as soon as Tom and Red find out about Liz's intent to give up the baby, they will intervene. As was stated in the latest episode, Tom does have a say in what happens to his child. Is it possible that he will end up with full custody somehow? Surely, Liz and Red would fight against this scenario.
Another possibility would be that the baby is adopted, but Red and/or Tom still provide protection to the child and the new family (with or without Liz being aware of it). This seems an unlikely outcome as the two men will resist the adoption and put an end to it if they can, but everyone who watches this show knows that the storylines rarely take the easy way out.