What documents should I request from a lingerie factory before paying a deposit?

Ask for the business licence, the most recent social compliance audit report with its date and the auditing body, the ISO 9001 certificate, and the OEKO-TEX 100 certificate number so you can check it in the public database yourself.

Then ask for two things that are harder to fake: production and shipment records for the last three months, and the contact details of two existing customers in your market. A certificate proves a factory was audited once. Shipment records prove it is producing now.