You need a agreement between both parties. Neither the regulation or commentary specify written, nor does they state verbal is acceptable. Most in the compliance industry (auditor, examiners, compliance officers, consultants, etc.) believe the agreement must be in writing to be able to disclose a rate lock agreement on the LE. I would suggest you do training and enhance your procedure to require rate lock agreements to be signed by both parties.
Reg Z Commentary 37(a)(13) states:
1. Interest rate. For purposes of § 1026.37(a)(13), the interest rate is locked for a specific period of time if the creditor has agreed to extend credit to the consumer at a given rate, subject to contingencies that are described in any rate lock agreement between the creditor and consumer.