Hi, I know what it's like to have friendship issues. I tend to be highly sensitive when it comes to attachments.
I think you should keep in mind that you being down probably has an influence on how you are feeling about your friendship with L. Also, though it is difficult for me to do I think it is important to understand that phases will come and go within the friendship. If you have an established "normal" with L. most likely things will balance back to that.
If I get too uncomfortable I am the type to try to have a conversation with my friend about how I'm feeling. But, sometimes as an exercise of caution (sense it can come across as too needy) I'll decide to not talk about how I'm feeling at least until I am absolutely certain that something weird is up. So often, differences like you are experiencing are more about perspective than anything else. You have to know, if you can, that it is not about you and trust that whatever draws you together as friends is still in tact. Attempt to shift your thinking away from feeling "unchosen" and hold on to your value as a friend. Most likely L. would not want for you to be feeling the way you are feeling right now.