I am definitely an introvert. That being said, throughout my career as a teacher, I often found myself having to spend a lot of after work hours engaged in any number of activities with a lot of people! Despite Lee preferring solitude herself, I believe she recognized the need to go with Carla to the bar to wait for the witness. Lee respected Carla as an investigator and while their personal interests were very different, I think Lee knew the value of her relationship with Carla. Sometimes, you do things you don't like to do to support your friends and colleagues. Sad to say, it probably isn't wise for a woman to sit alone in a bar these days as well. Lee seems to be more comfortable spending time with men. I think it was important that she went as a way of continuing to move forward in her own life- -and nurturing a friendship with another woman.
Due to the fact that Carla and Lee worked so closely on a number of cases, I feel certain Carla knew Lee was questioning her abilities after losing her last case. I think some of her attempts to engage Lee in more social outings was an attempt to be supportive and encouraging- -keeping Lee focused on something other than whether she "still has it".