Pretty sure the LBD is specifically stated to be using a percentage of her power constantly to keep those she mind + soul donuts in check/under her/taken into her powers. If its Zamasu’s semi-immortal body, she’d be able to affect him (he only massively scales off of 3 Uni), but once Zamasu casts it off he envelops the whole hypertimeline (putting him far beyond her level of power) and as such should be too much for her to attempt that on. Not to mention his Immortal Soul (what is left after he casts off his body) is an abstract, and I’m pretty sure we have no evidence her Soul Manip works on that.
Essentially, LBD could totally ensnare him early battle, but late game he becomes beyond that. (This also applies to her sealing of souls. His Soul is just something beyond what her sealing has shown the capacity to do).
Zamasu negates durability with his Sickle of Sorrow, so the state advantage she has isn’t really going to matter unless she lands a blow, and she can’t really get hit in with his really great and all encompassing Ki barriers, blast waves, clones, etc. While she could dispel the clones, they’re infinitely generating from his rift, and she can’t do anything about that (so she’d have to continually dispel them).
Since he has Goku’s powers, he should be able to sense her attacking his mind beforehand and could potentially stop her, but he has no direct counter to that.
Any damage she does won’t be effective due to his immortality so long as she doesn’t paste him on the molecular level (and she typically does play with her food, and I don’t think she can regardless).
Zamasu’s Ki senses, awareness, etc. should allow him to get around her illusions.
With Instant Transmission he can teleport at will, so BFR won’t work.
This means her main forms of attack are limited to playing on his fears, corrupting him, and, well, hitting him. Problem is, Zamasu’s mind could probably see her mental attacks coming (but could not defend against it directly) and he’s WAAAAY better at fighting than her. She literally almost entirely despite all her powers to Wukong due to just his fisticuffs, and only used her possession type power on him at last second (which means she wouldn’t start with it anyway).
He could also probably sidestep her mental attacks by simply time traveling (ceasing to exist so her mind attacks have no target and appearing in the future to attack her). Also, his omniscient vision and Ki Sensing mean her teleporting away doesn’t matter.
That said, without that scythe (or Infinite form) Zamasu can’t hurt her, making his primary forms of attack irrelevant, his defenses can be broken by just punching with all her force, and if he doesn’t end her quickly she’ll just possess him or attack his mind and leave him beaten if she catches his mind before he can react to his sensing. He can also actually probe her mind first, but he’s never used it in combat.
I think I’ll vote the Lady Bone Demon in a pitched battle, unless someone provides a more surefire means Zamasu can immediately access to defeat her, since unless he goes full Hypertimeline Sore Loser, she can beat him pretty quickly in ways that don’t trigger it (which destroying his body would do) so long as she fights more seriously than normal.