It's hard to know what a payer means by 'not an acceptable diagnosis code'. As I see it, there could be one of two things going on here. The payer may not consider this diagnosis to be a medically necessary reason to perform a biopsy. If that's the case, there should be a published policy or LCD that specifically states this. Clearly your providers would not agree with this, and it may be possible to appeal the denial. Whether or not you can bill the patient will depend on the payer's guidelines, your provider's contract with the payer, and/or whether or not you have obtained a waiver from the patient. The other possibility is that the payer doesn't consider this diagnosis to be appropriate coding for a biopsy procedure. In that case, I would be arguing with the payer because there is no coding guideline the prohibits the use of this diagnosis with the biopsy codes, and in fact if that's what the record gives as the provider's diagnosis, that's what needs to be coded. In this case as well, you may or may not be able to bill the patient depending on your provider's contractual relationship with the payer.
I'm not aware of any LCDs that actually limit the use of biopsy codes to just certain diagnoses. You might look at the 'benign skin lesions' LCDs, but those usually just involve excision procedures and not biopsies. Biopsies and minor and inexpensive procedures and I can't imagine why a payer would have a problem with this.