They can ask for anything they want, but you are under no legal obligation to give them anything related to your AOS processing beyond your receipt notice and your EAD card. Also, if the EMPLOYER's lawyer is asking for this, I'd be concerned about a conflict of interest. Tell the lawyer that you won't even consider giving them such documents unless and until they assure you in writing that they accept all liability, known and unknown, for anything adverse to you that might result from such disclosre. Of course, they will refuse. When they do, ask them why and tell them that if they are unwilling to assume responsibility, you aren't willing to make disclosure.

If they withdraw their employment offer, you might want to consult an employment attorney about suing them.