She is damn near impossible to get approval up while you are being good,
this is just copy-paste from the wiki,
APPROVAL UP:
Show Guex in the Druid Grove your sword fighting technique (Athletics check).
Talk to the bird in the Druid Grove by using Speak with Animals and intimidate it. (Charisma check).
Convince Zorru, in the Druid Grove, to kneel.
Choose to attack Taman and Gimblelock in dialogue outside the Crypt.
When talking to Zevlor the first time inside the Druid Grove, tell him you're sorry but you have no time to help him.
During dialogue with Lae'zel, after she describes ceremorphosis, tell her you will find a cure.
If Kagha's snake kills Arabella, tell her "She was just protecting her own." in dialogue afterwards.
Swear to Nettie you will take the poison.
Crush the Tadpole outside of the Druid Grove.
Decline the Devil's invitation to remove your Tadpole.
Respond to Volo in the Goblin Camp with "-"
Make Novice Crusher kiss your foot in the Goblin Camp.
Resist during the first dream sequence.
Cruel behaviors.
Calm down the boar near where you recruit Astarion.
Fight the fake god Boooal in THE FESTERING COVE.
Allowing her to speak to her githyanki brothers/sisters
When the player emulates the roar of a mind flayer while talking to Lorin.
Break Alfira's lute.
Acknowledge how valuable the K'liir library is.
Drink from the well in the Putrid Bog (Quest: Save Mayrina)
Kill the Owlbear cub and its parent
Reassure Lae'zel in the Camp that she will survive and please Vlaakith
APPROVAL DOWN:
Convince the Owlbear not to kill you in its cave
In the crypt, agreeing with Shadowheart, questioning the need of possessions for the dead.
Convince Arka to spare Sazza by stepping in front of the crossbow.
At Camp, agreeing with Shadowheart that the first priority is to find a healer.
Try to persuade the goblin guard outside the Goblin Camp
Smear dung on your face when Sentinel Olak askes you to
Lae'zel has a rivalry attitude towards Shadowheart, heed to Shadowheart's advice will upset her.
Sympathetic behaviors.
Disapproves if you succeed in the persuasion check to stop Kagha from imprisoning the child.
Find the evidence of Kagha working with Shadow Druids and expose her. (Quest Save the refugees)
Bring Mayrina back home (Quest: Save Mayrina)
Make a deal with Auntie Ethel to remove the Tadpole from your brain (Quest: Get Help from Auntie Ethel)
She generally disaproves if you dont like killing things. She likes killing things and solving things by killing. She dislikes you doing things which could be solved with a fight. If you don't like doing that she is written so she does not like you. I agree there are a hadful of oddites in the above, but generally it fits her character well. It's "damn near impossible to get approval up while you are being good" because she as a character does not like you if you do those things.
The other issue, though it has been toned down is that one of the ways in which the approval-disapproval dynamic is done is that things that grant Shadowheart approval grant lae'zel disapproval and vice versa. So you can't really get them both up without doing some really meta-game things.
There is plenty of nuance in her character, but it is tied to her insecurities and hopes for the future, not her understanding of good and evil. I hope she stays who she is.
