This page of the Baldur's Gate 3 guide has a walkthrough for a Get help from Healer Nettie quest. This solution will help you to complete the quest.
- Find the healer - Nettie;
- go with Nettie;
- find an antidote to the poison.
If you manage to resolve the Lea'zel's quest peacefully in the cage, there will be an additional skillcheck for persuasion. If you pass it, you'll find out about Nettie, a druid's apprentice who can help you remove the parasite.
You can found her in the Druid Grove, specifically in the Emerald Grove (M3;18). Go to her and tell her about your problem. She will be able to help and tell you to follow her to the designated place.
When you follow her, you'll get to a room where another conversation will take place. This time, Nettie will offer you a "cure." If you pass an investigation skillcheck, you'll realize it's a poison and refuse in time. Then, if you can pass the persuasion skillcheck, she will let you go.
However, if you decide to take the specific, the character will be given the status of "agony". To take it off, you'll need an antidote. If you successfully pass the aptitude skillcheck, she will give it to you peacefully. Otherwise, you'll have to fight and take the antidote by force (you have to search the corpse). Then you have nothing else to do but to leave the room.