Elephant lamp = MC was in the guy's private quarters/study room, which is more progress than her sister (who wishes she was intimate with the guy), so she can mention details about it that her sister doesn't know, such as what kinds of furniture there are
Dragon lamp = sister tried to claim she knew about the elephant lamp by saying it's gray, but MC intentionally jokes and says it's actually a black dragon, showing she knows more about it (by being closer to the guy and having really been in his study) than her sister