I've tried to be strong but I feel like I'm not making progress, I've started speculating about the future by myself and can only see loneliness. I don't want to be her best friend but it did feel good being with her again.
I think you handled yourself very well. What you don't know is how she was feeling during and after this meeting with you. When the LBH has a chance to show his positive side (charming, smiling, upbeat, in-charge), it can pull at the heart strings of the W. The LBH may never know about some little way he looked, smiled, said something, etc. that triggered buried emotions in her. And this is a good thing to leave her thinking of you with fond memories.........that can lead to fond desires.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!