By default, Lightspeed prevents users (except managers) from finalizing the orders of other users. Deliverect uses a dedicated virtual user to process online orders. Therefore, if this role isn't assigned to employees, they will not be able to finalize online orders.
To change this setting, follow the instructions provided in this article from Lightspeed.
The specific user role needed to finalize other users' orders is named Allow edit receipts other users.