If your friend is actually a TRUE friend, then talking to her about it won't ruin the friendship, it will make it stronger. Obviously, you can't own your friends. You need other friends, just like L. does, otherwise there is no room for growth. If the two of you don't explore friendships with other people, you are holding each other back from potential learning experiences, since everyone has something special and different to offer. If it were me, I would give L. a call and tell her that I miss spending time with her and would like to hang out more often. If you are direct and honest about your emotions, it is likely that L. will understand and make an effort to spend more time with you. If she is upset about your feelings, she will either get over it in a few days after she has had time to think about it and work through her own possible feelings of guilt for hurting you, or she will prove to you the depth of her friendship and loyalty to you. Either way, you will know whether or not it is a good idea to invest more time and emotion into your relationship with her.

What ever you decide, don't dwell on the possibilities. Take action, based on how important the friendship is to YOU. If you truly value her as a friend, then being honest with her is the best thing you can do. If you look into you heart and realize that you don't value her friendship as much as you thought you did, and are more concerned with the withdrawal or rejection you feel from her, than it's best to move on and take the friendship to something more casual/superficial. People will always flow into and out of your life because our paths through life do not follow a linear pattern, but they rather weave - they ebb and flow. There may be a reason this friend needs distance from you at this time in her life. This other friend might have a lesson for her, and when that lesson has been realized, your friend may find herself drifting back to you to continue the closeness you once had. Friendships are everlasting, if you nurture them. But you have to be willing to let the other person lead their own life, even if what they need differs from your needs at the moment. Friendship involves understanding, loving, and accepting. Understand and accept that your friend is exploring relationships with people other than you, and have FAITH that those relationships do not imply replacing you, and are not a threat to you. If you have a true friendship with L., she will find her way back to you when she is ready. Talking to her about your feelings will help you vent, and also help her evaluate the role that this new friend has in her life. Either way, it will ensure that you do not resent her for your perceived abandonment, because you made your feelings known and let her make her own choices.

P.S., I have had friends that have lost touch with me for years, only to pop back up in my life later. Some of these friends, when they returned, helped me realize that their friendship was not healthy for me and that the loss of the relationship, although painful at first, was for the best. Other times, the friend returns to my life only to pick back up where we left off as if we had never been apart. Stay open to what comes, and don't worry about the things you can't control - and you cannot control other people, or decide what their needs are for them. You also cannot expect them to fulfill your needs.

Hope this helps. It's a difficult thing to let go of something that we want. From a Buddhist perspective, enlightenment comes from endeavoring to cleanse yourself of "wants" and simply accept what "is". Just the act of reminding myself to do this has helped me get through a lot of situations like this, since I am a very jealous and possessive person. It's a battle, but I wish you the best and hope you find a way to make peace with this legitimate struggle.

Good luck :-) Hugs!