Where can I find the information stating the LENDER is responsible to pay for a appraisal that was ordered thru them?
The appraisal was ordered presumably in good faith by the lender for your benefit. Lenders do not order services unless they are acting on someone's behalf. However, when the lender orders an appraisal, they become a client of the appraiser. Once completed, the appraiser sends their report to the lender along with an invoice made out to the lender. In short the lender is resposible to the appraiser. Now this same lender has incurred an expense on your behalf. Assuming that the loan did not fund, there is an open invoice for that appraisal. The lender should pay that invoice (since they are the client), then they may pursue the borrower for reimbursement (for services rendered).
Lenders typically require borrowers to pay for appraisals at time they are ordered since lender is resonsible for paying for the appraisal once it's completed, even if property value is insufficient or borrower decides not to close loan. Federal law requires lenders, rather than borrowers, to order appraisals, and lenders pay the appraisers for services rendered, but the borrower is still ultimately responsible for the cost of the appraisal.