When you open a Gacha (Lucky Box), the items will not be sent to your inventory directly but to the special Gacha Storage which are like temporary extra inventory slots.
To check your items, open the Gacha Store and tap the Item or Pet Gacha Storage.
You can also access your Pet Gacha Storage from your Guardian Pet menu.
(↗ menu -> Pet -> Gacha -> Check 'Pet Gacha Storage')
Note that once you collect an item from the Gacha Storage, you won't be able to put it back!