I have to agree that asking you to go to back to condoms in a 10 year relationship is likely asking for too much. (I am unclear - are you fluid bonded with her too?)
However, I wonder if L would get her needs met another way? She seems to be searching for a way to feel special to you, to be someone unique in your life. I realize you already feel that way about her but perhaps talk with her about ways to help her feel more special/unique in your life. It might be really helpful to you both to dig down to the reasons and emotions behind the request.