Every warning Shadowheart gives about Lae'zel is probably true. She is a githyanki, a race of people who believe in plundering what they want, when they want, and any roundabout ways of solving issues is weakness. They are raised from birth to fight and kill and they probably do so on reflex. To her, being diplomatic and not domineering is like watching a parent placate a spoiled child. Pathetic. She is intense, severe, and excessive because she is a gith, and I love it.

The nuance with Lae'zel comes from emphasizing the "lawful" in lawful evil alignment. Order, hierarchy, procedure, and honor are some things you can appeal to that don't always require wreaking havoc on the weak. Resisting the tadpole every chance you get earns respect from her. One of her best scenes is when she thinks ceremorphosis is inevitable and is willing to
take her own life than turn.

Approval is also not even a big deal. Her greeting only changes when you get Exceptional Approval or complete the Gith Patrol. Approval really isn't going to change her tone in EA at the moment. But if you want her tone to change when you speak to her, it depends more on what you choose to say than anything else. She can come off as someone you can actually work with, like a business partner of sorts, if you keep chatter to information and the current situation. Notice how much information Gale unintentionally gets out of Lae in banter.

On the flip side, it takes A LOT to get the companions to Very Low Approval for them to leave you. I think playing an unyielding, forceful lawful good character would make for an interesting dynamic between them and Lae'zel. You keep her around because she's an effective warrior whose one job is to eliminate targets, and she sticks around because you get things done. Approval wouldn't be very high, but tension is one of Lae'zel's selling points. Also, Lae'zel reacts if you
sell out Astarion to the monster hunter,
and one of the responses you can choose seems very lawful good. Her response to that option makes for interesting characterization for the player character and it has intrigued me to make this character type ever since. Of course I am currently thoroughly enjoying playing in a way more in line with Lae than to change it up at the moment.