As someone else said, the adventure and session will provide most of the context for most NPCs regardless what you put on the statblock.
And that context makes the LE part unnecessary.
Beyond that, I know she keeps her word, doesn’t value others’ lives or freedom as a “good” in itself, is willing to work as part of a system/hierarchy, and combining my own life experience with what LE means, she probably has a visceral distaste for liars, and people who break rules, and is completely willing to hurt people for small “infractions” because she believes in the power of negative reinforcement.
Does that mean it? Lawful doesn't mean that one has to always keep their word or that they hate liars or rules-breakers. That's why devilish contracts are renowned for having loopholes, double-speak, and obsfucated phrasing. My own life experience with "LE" people (such as at my former workplace) suggests that they will do whatever the heck they want as long as it
looks legitimate and can be justified to others, whereas "CE" people don't care about appearances.
About the only part here I agree with is being willing to hurt others for small infractions--but that's something that CE and NE people will do as well.
I looked up "what alignment is Darth Vader" and most people seem to think he's lawful evil--but he had no problem altering the deal (and telling others to pray that he doesn't altering it further). So, lying and rule-breaking right here. Has the internet lied to me?
And I'd say that the information you provided is
barely enough to RP her. How does she act to the PCs? Does she play along with them and then abandon or betray them later on? Will she work with the PCs completely, no matter their goal, because she's "lawful" or will she try to stop them if she disagrees with them? Does she insist that they kowtow to her? Will she accept one of the PCs as the leader, or betray them? How small of an infraction will she punish, and how far is she willing to go? See, the answers to these actually both provide useful information
and replace the need for an alignment.
To me, that shows that since we seem to disagree strongly on two out of the three aspects of what you consider to be LE, I think this goes even further to show that alignment is not actually helpful.
But assuming all the stats are provided: LE tells me if she gives her word on something she'll keep it, she probably values power and takes careful note of who outranks who (and by extension, where she fits in the pecking order). Her level and power (including availability and-or power of allies), relative to the party, will determine her approach: if she thinks she's in a position of power she might haughtily offer a bargain (which ends up in her favour, of course); while if she's clearly outgunned she'll have a getaway plan in place and use best tactics to defend herself while escaping. Location makes a difference as well: if the encounter is set in her home or lair her approach will be different than if she's met in a tavern or in the wild.
Howzat?
As with the "punishing infractions" from above, most of this works just as well for NE, CE, and LN beings. If our mage (who presumably is intelligent) here was one of those alignments, she's still going to value power, she's still going to take not of who outranks who, she's still going to have a getaway plan whether she's lawful or not. A low-Int chaotic or neutral evil creature might be more gung-ho, but once you get to above-average stats, nah. The only real difference between alignments here is that after her sudden but inevitable betrayal, a LE person might view killing the party as a chore that needs doing and the CE person might have more fun with it. Maybe. And I still disagree that "lawful" means "honest," for reasons stated above.