@nobaka
Not wanting to die isn't cowardly, but it's a bit out of character for Liz to be so passionate about it after being so blase about it earlier. Back in chapter 18, she said she has no reason to live or die, and only lives for orders. (If anything, the system of slavery is at fault here, but that's beyond the scope of the observation.)
Not wanting Shingo to die isn't cowardly and it might be true that he's incredibly important, but that's not her argument at all. She says "I've been ordered not to kill you." Which implies that were it not for her orders she wouldn't have any problem with it. She says that if he dies, then she'll be killed. She doesn't say that if he dies, then it'll be a loss for the world.
She says that his specialized knowledge amounts to tedious conjectures, and doesn't seem to think very highly of it.