discussing tlh/chot again has reminded me of the entirely different version of it that exists in my head. like hear me out, what if Lilith was the one aiding Tatiana instead of Belial???
Lilith, who's greatest wish forever denied is have a child. Who upon hearing that a warlock, a so called Child of Lilith united in their inability to have children, has done the impossible and she's outraged. She wants nothing more than those children, who should have never been born, to be wiped off the face of the earth and history altogether.
so when a woman who shares in her hatred calls upon her its almost a sign. she's just as foolish as her father, and hates them for petty moral reasons. she's usable, and will do what Lilith wants - destroy the Herondales. Grace is a pawn for them both, a destroyer groomed from childhood.
Belial in all of this is not an antagonist. He's still cruel and worthy of the title of Prince of Hell, but he's... got a little soft spot. Mostly it's the bragging rights, for he is the very first and only denizen of Hell to have grandchildren, a legacy. He managed to do the impossible and to protect that he's willing to help James and Lucie if they so ask. also.... he's still the reason Jesse dies, his warning to Lilith and her games.
When Tatiana wishes to bring her son back, Lilith helps her. Not as a part of her plans, but out of sympathy (or her version of it) because no motivation is more true for her.