How to handle situation with insecure friend(F29)?

Ive (M27) been in this city for about 6 months. Ive been able to make great friends here. My closest friend (F31 call her Vicky) is someone i hangout with alot. She lives nesr my job and i help her walk her dog alot. She has 2 roommates, the first (F26 call her Emma) and the secnd (F29 call her Liv). All three roommates grew up in the same small town and their families are very close. Out of the 3 girls im closest to Vicky, but Emma is a close 2nd since we sre similar age and sometimes hangout. I like Liv as a person alot but she is more reserved. She Likes being at home which there is nothing wrong with, i used to be a homebody but i want to experience new things in this city so i try to go out as much as possible. She used to go out but lately has just stopped going out. I enjoy her company but we just dont have the connection i have with her 2 roommates.

Talking to vicky, she says that Liv has alot of insecurities. Recently vicky has been having problems with liv. Im not sure what it is exactly as vicky doesnt get into details and i try to stay away since it seems like a roommate issue. What i do know is Vicky has mentioned how Liv can get very insecure and gets upset when she feels certain jokes are aimed at her.

The other day the whole friend group was hanging out. We were having a great time and making jokes. I made a small joke that was not directed at Liv but hit one of her insecurities. It wasnt a degrading joke in any way. It wasnt a joke it was more like a general statement. When i look back i see her walking out the door. Some people who know liv longer than me told me she is insecure about the topic i joked about. I immediately rushed to get her before she left to apologize, she saw me and kept walking and when i reached her she said she didnt want to talk to me and left. So i told her i understood and apologized.

I havent seen her since. I told vicky and liv what happened and they said the joke wasnt bad and they said all their friends who heard the joke didnt think it was bad. But i felt bad cause i like her as a friend and dont want to do anything to hurt her feelings. A few days have passed since then and i have accepted that i did alot to try to mend it and i have to focus on what i can control and use this as a learning experience with Liv. I havent been to Vickys place and i told vicky that i think its best i dont pass by for a few days (maybe a week) cause i dont want to cause more issues. Vicky and emma are mad at liv because they feel Liv is being immature and they say they enjoy it when i visit them and dotn want me to feel uninvited. I told them i just want tk give liv a few days and i expect to be back soon. Inalso said liv has a right to be mad, i understand why she is mad and even though the joke wasnt as bad as she thinks i couldve kept it to myself and i dont want her to feel uncomfortable in her own home.

I dont think the friendship is over, i think its just a rough patch. But when we do talk again, i want to hear her out and understand why she felt it was a bad joke. How can i better handle this situation with Liv to avoid this in the future? Ive decided im not going to make jokes around the topic but im not sure what all her insecurities are so i cant guess.