@Rachelharris31 Thanks so much for testing all of that & it's awesome that you tested both on PC and console. I hope many other players will benefit from reading your post if they have this same issue in their game and decide to research it here on AHQ. :D
I have been doing further testing on my Lilith Vatore and unfortunately even without the Withered Stomach weakness she is still doing that "plasma juice pack" animation and appearing like she is about to be sick (as shown in the images I added in Post #1). I previously used a Mod to delete all of her Weaknesses and this time I chose Eternal Sadness, Nightmarish Sleep (counts as two weaknesses), and Guilty Drinker. Lilith occasionally did the "crying" idle animation but she continued to do that other plasma juice/low thirst animation as well. Her Thirst need was nearly full and she is only using plasma juice packs or other Sims for feeding, she is not eating any regular food or plasma fruit food recipes. I'm beginning to wonder if there really is something different about Lilith. She doesn't seem to be getting the +3 Sadness moodlet quite as often so maybe before it was just a bad streak of frequent random occurrences-- or maybe the Withered Stomach weakness made that worse too?
I've cheated her back to zero weaknesses for now & I will try some different combinations the next time I play. I'll also try what you suggested with using Vlad or my other vampire instead of Lilith & hopefully I will have better luck with them.
EDIT: So far the only way I've been able to prevent Lilith from constantly doing the crying or the angry/low thirst idle animations is with mods. I've been playing Vlad's household for the last 28 game-days. I've given him the same Weaknesses as Lilith and he never does any of those idle animations, just a lot hissing.
EDIT 2: I've added a teen daughter for Vlad's household. She was a regular Sim I created in CAS and turned into a Vampire through game-play. As she has been leveling up in Vampire ranks I have been giving her the same Weaknesses that Lilith has. This new Sim does not do the same "plasma pack"/ low thirst idle animations as Lilith does. I am not using any mod cheats on this Sim. I'll keep adding more of the same Weaknesses all the way up to Grand Master Vampire and see how it goes.
EDIT 3: I am still trying more vampires and so far it's only Lilith with these problems in my game. I've spoken with other players who also seem to be having similar issues with Lilith.