Why isn't Lust covering up her tattoo?
I've only seen the original anime, so I might have a wrong idea about her personality (and thus motives). My first guess is that on the train, she's just in the general public and has no reason to cover it up (not to mention the outfit looks like it shows some cleavage, which might be helpful and seems to be in line with her personality) while for the date she covers up to hide the mark from the military who may or may not know about it. Even if they don't, it's definitely an interesting mark that would draw attention.

My second guess is simply that she covers up on the date to look more modest and less "slutty".