She is doing a lot of this for attention, and negative attention is better than nothing. You have two other children (13 yo bipolar/9 yo Aspergers) and the 15 yo is having to deal with having siblings who require enough attention that she feels she's getting the short end of the stick. This isn't rocket science.
With the boyfriend: She knows this boy isn't good enough for her, but the fact that it bothers you is enough for her to continue seeing him. If you seem not to care if she dates him or not, she might not "date" him anymore. BUT regardless of who her boyfriend is (this guy or someone else), there still need to be established rules in place. They can watch TV or hang out at your house, SUPERVISED, or go out with friends, but that's it. No sleepovers, etc.
AND...if I asked my parents about sleeping over at a friends, my mother would call the friend's parents to make sure they were going to be there, what was going to be going on (movies? Popcorn?), and what the plans were for the evening, and when I'd need to be picked up. Why didn't you do this? You know she lies, you picked this time to believe her, then ground her for a month because you didn't take the time to check her story out? (Just saying that the responsibility issue is a two way street. It's her job to behave responsibly, and yours too.)
Consider this: If she's sleeping over at his place, there are other things she's likely doing that you don't know about too. Like Dr. Phil says, "For every rat you see, there's a dozen more you don't see." Drugs? Alcohol? Other stuff?
Further: My mother always says, "You are who you hang out with." If she's hanging out with rats, then....
Further still: Yes, everybody needs ways to cope with "stress" or whatever issues they're dealing with. The answer is NOT always counseling. Sometimes it's taking part in team sports. Her friends do but she doesn't....hmmmm...what's up with that? Sometimes counseling is the way to go, but it isn't the ONLY way to go.
Reel her in; tighten the leash; whatever you want to call it, but be on her like glue. Where is she going? Who is she going to be spending time with? What are they going to be doing? How long are they going to be out? If there are any answers that are in any way questionable (if her body language and actions don't fit what she's telling you), then don't let her go becuase something's up. Your job is to know where she's going who she'll be with, what they're supposed to be doing, and for how long. AND have the friends come meet at your house - when they get there, ask one of them, "What was it you guys were going to do? How long where you planning on being out? Do your parents know where you're going to be?" See if you get the same response from them that you got from your daughter, and don't be afraid to tell them in front of dear daughter, "You know what, I just realized that (insert daughters name here) won't be able to go out with you guys today. I need her to help me with a special project."
Let her know there are consequences to her actions, and if she chooses to do things she knows will get her in trouble (like lying about sleeping over at a friends to be with her boyfriend), then there will be consequences, and she isn't going to like it either. Further, her actions are hers. It isn't anyone else's fault that she chooses to act the way she acts or do the things that she does, so don't let her guilt trip you into thinking it's your (or anyone else's) fault she is behaving that way.
Now - all that aside...you do need to spend some QUALITY TIME with her. Take her out to lunch, just you and her, to her favorite place. What does she like to do? Maybe she'd like a manicure? Does she like to go shopping? Is she artistic? Do you know what her favorite color is, her favorite restaurant, or even her favorite game to play?
NOTE: It is VERY important for her to know that even though she isn't bipolar or have Aspergers, that she's still a valuable part of the family, she's still worthy of your time/love. (OBVIOUSLY this isn't being made clear to her because if it was, the other areas in her life (grades, lying, etc.) would reflect that. Again, she's at a point where negative attention is better than nothing.)
For what it's worth, and good luck!