If I lock my joint card, will my joint account owner be able to reactivate our joint card on the app?

No, unfortunately with this app there can only be one primary device that is able to set controls for the card. Both account owners will be able to see the card and card transactions in their apps but only the primary device will be able to set controls or lock the card. The primary device which locked the card will be the only one who can unlock the card again.