Each order requires that a user be assigned to it as the buyer, and each user has a Receive Orders setting to determine how orders assigned to that user should be received. You can choose to "Receive through Retail" or "Receive through App". For more details, check out the user management chapter for more information on the "Receive Order" setting
First, check if the order failed to send, in which case you'd find it under the Sending / Failed to Send list.
If the order was successfully sent, the issue may be the assigned buyer's "Receive Order" setting. If the buyer is set to "Receive Orders in Retail", then as soon as an order is sent from the app, it expects that you'll be handling the receipt of the order strictly through your Lightspeed Retail software. Orders like this are shown under Archived Orders>>Receive in Retail after they have been sent. Check out the user management chapter for more information on the "Receive Order" setting.