You're in the right place for sympathy and advice!  My SD61 is a lifelong liar and I'm positive she's lying to her therapist, as she does to everyone.  For therapy to work, 2 things are necessary:  desire to change and honesty.  She doesnt really want to change, wants support for her dysfunction.  

Your SD is young, I hope she can straighten out.  You've put a lot into your family, you deserve better.  But, this is steplife....

Damn. I'm sorry you are going through this. One thing i will say as the parent of a teen girl and as a former teen girl - they love drama. Anything that increases the drama. My daughter did something similar to me a few years ago - lied to her doctor and said i was harassing her about her weight when in fact it was her dad doing it. When i asked her why, she said it was because she was afraid to tell on her dad but she wanted to tell someone it was happening. Lucky me, i guess i'm the "safe" parent. I guess you are, too. You are giving so much to these kids and caring so much. That's a dangerous thing for a stepparent to do, as you get so much less in return than a bioparent does. Bioparents get bonus points just for existing where steps have to earn their place. 

**My husband and I both had a long talk with her about lying and all the repercussions this is going to cause.... he doesn't think it's fair to ground/punish her for her actions.**

Your husband is wrong.  If there are no consequences for her lying, she will continue with her lying.  She might continue anyway, but by not providing consequences he's affirming the behavior.  I'd be especially worried because the BM is a liar and may encourage the SD to lie to hurt you, cause chaos in your home or achieve some custody or CS objective.  In the past it's been lying to her mother.  Now it's lying to the therapist about you eavesdropping.  Next it could be false abuse allegations.  Stepkids who lie about you are dangerous!  Luckily you have no bios who can be taken away - would an abuse allegation affect your livelihood?  If so, get the cameras up now, because a lying child who receives no consequences is going to continue lying, and you never know how she'll ramp up or what she might accuse you of.

I hope when you say you've spent $400,000 on legal fees and GAL expenses you mean that your husband has spent that money.  Your money should not be going to his custody and related battles.

Do you actually think BM will let her daughter run around braless ?  Or clothing two sizer too small ?   You are doing things because you want to.  The kids want name brand, and BM will not spend the exter money for name brands.  
If SK lie and stab you in the back.  Disengage, stop doing for SK's or SK.   There BH and BM kids, let them handle it

I started my response and deleted it several times. The reason being that I'm really emotionally-charged reading your post because when it comes to lies, I just won't fucking tolerate it. I had a bio I could have lost and my entire career ruined, so there was no way in hell I would tolerate letting lies slide. 

Your DH needs to spell out to your SD the entire chain of events of the devastation of lives that could occur as a result of allegations. Do not let your DH let it go. If he pulls the bullshit excuse about how he doesn't want to consequence his lying brat in case she won't go to him if she's really abused, stand strong and tell him it's pure bullshit. She's learning that it's OK to lie. She's learning to up the ante because she didn't quite get the big bang result she wanted. So, next time, it'll be a doozy. 

Also, with all due respect, why is it you forking over so much money? Paying over 400K in attorney and gal bills is not your concern. It's DH's "shit" to handle. Also, why are you the one encouraging therapy and finding the life coach for your SD? You buy them clothes, etc. You admitted to being exhausted. What is your DH doing to show appreciation for all of that? Is he throwing himself at your feet and worshipping you? Because if I was doing all that you're doing and not getting much in return, I'd have a major problem with it. I don't see in your post where your DH is doing anything useful of his own volition or showing you appreciation. I could understand you doing all that you do if you were being rewarded for it, but since you're exhausted, that means that you're over-functioning for little to no reward. Believe me, I understand because I've been there. Until I wasn't. After decades of doing what you're doing with no reward, no affirmation from my DH that I needed so badly, and crappy treatment from my SD who ended up shunning me in my own home for over 7 years and not one person standing up for me, I threw in the towel and totally disengaged. I have not spent one cent on my SD in YEARS. I have not done one household task for her in YEARS. DH has learned to kiss my royal ass like I deserve. I will no longer be overlooked, ignored or be invisible in my own damn house or family. I highly recommend disengaging. You're not being rewarded or appreciated, so you'll have to reward and appreciate yourself. You might want to have it out with your DH if he isn't showing you that he values you. From what you say in your post, I think that your DH needs to step it up as both a father and as a spouse.

Cripe - 400k? Chit.

Thats like 5 college educations. 

Disengage. Shes going to get you in trouble with her lies. Let her go. Dont keep fighting with BM. Its super duper not worth it.

Part of parenting is preventing  minor children from harming themselves.  That includes serving themselves up as a victim to a domineering asshole "boyfriend"... particularly not at 13yo.

smh