According to this login, you should be able to find your shopping record, but there is no order number in it.
Lotte, like Taobao, has many other businesses selling it, and Lotte only acts as an intermediary. After you place an order, Lotte will send an email of the order to your registered email address. I wonder if there is an order number on it. Then on the same day or the next day or one day, the merchant will send you an email to inform you that the goods you want have been sent out. There should be relevant order information and the approximate arrival date, and the courier number of the courier company is all on it. Using this number to go to the home page of the courier company should be able to find out where the goods are sent! I guess this is what you want to check.