Lightspeed by default prevents users (except managers) from finalizing the orders of other users. Our system 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, you can consult this article at the Lightspeed Helpdesk.
The specific user role needed to finalize other users' orders is named 'Allow edit receipts other users', as pictured below: