Like all alignments, Lawful Evil is commonly argued about.
Some people think it means you follow the laws of the country you are in, but you twist or pervert them to exploit others; e.g. a bureaucrat.
Some people think it means that although you are essentially evil, you have a strict personal code that is recognizable as such. One that you follow even if it is not totally advantageous. For example, perhaps you value your word of honor, even though you have no qualms about murder/torture/etc.
Others think that it means you gravitate towards using collectives/organizations (likely with their own customs/rules) rather than being a pure individualist just in it for himself. Certainly, many Lawful Evil monsters in the Monster Manual fit this criteria. They are clearly not following the laws of the land, but they have their own hierarchical structure that they respect. Mobsters would also fit this definition.
This is why, as a DM, it is always a terrible idea to try to "enforce" alignment. Your idea of what someone's alignment ought to be is different than their idea.
Pay attention to behavior, and if there are some specific, clearly defined behavioral requirements, then you can "enforce" those. e.g. Paladin oaths tend to have a few pretty clear actionable items. If you as DM state a game is not going to allow some specific thing, like no sex, or no torture, or whatever, then that's a behavioral item you can enforce.
But enforcing someone's alignment based on your interpretation of it? Nah. Recipe for unnecessary conflict and emotional outbursts. As demonstrated by Downlowd's extremely visceral response to this plan. My reaction to this plan would be very different. I'd let it play out, with success or failure (or success followed by swift retribution) left entirely up to what defenses are in place, what methods the heist uses, etc.
If it resulted in the thief being killed, or the whole party being killed... okay. Shucks, time to roll up some new characters. Not sure what the big deal is.
I don't specifically see much point to the endeavor, but it's also not particularly a huge red flag or anything.