if the BBEG is cornered by a paladin next to a pit of lava and they can grab an innocent child as a hostage they will. They may well give the paladin the choice of jumping in the lava themselves or throwing the child in. Because the BBEG is evil and will exploit any weakness they can.
One reason this is unlikely IMCs is that I typically use a Projection-based Theory of Mind for NPCs. The villainous NPC typically assumes that other people are 'really' the same as they are - equally vile, only weaker, more hypocritical etc. So it will rarely occur to them that the Paladin will jump in the lava at their behest unless the paladin has somehow already made that clear.
Edit: Like you, I also avoid designing encounters to screw with particular PCs. A random dragon is a random dragon, I don't send a dragon to torture the Paladin while letting the Rogue off free - or vice versa.