From the Super Mario Wiki
Princess Lipid is a strange white figure that appears in Mario & Luigi: Bowser's Inside Story and its 3DS remake, Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey. She speaks in Early Modern English, also using nosism, like the Honey Queen. She states that she controls Bowser's mucus membranes. Her name is derived from the word "lipid", which are a group of molecules such as fats and waxes.
While chasing after Princess Peach when she is captured by Alpha Kretin in Flab Zone, Mario stops in front of a bridge over a section of mucus while Luigi attempts to cross. Mario stops Luigi, but the sections of the bridge fall, causing him to fall into the mucus below. However, Princess Lipid then emerges, holding both Luigi and a treasure chest containing a "treasure of e'erlasting wonder". She assumes Mario dropped one of the two, which Mario affirms to be true, but before he states which, Princess Lipid makes the conclusion that Mario dropped the treasure chest. Mario quickly states that was not what he dropped, explaining that Luigi is his brother and is more important than any treasure. However, as a result of Mario's honesty and loyalty, she gives him both Luigi and the treasure chest, then descends back into the mucus. The chest contains 2 badges: the Good Badge and the Mushroom Badge, as well as a Tenderling. While the bros. are in battle, Princess Lipid appears again and helps the player learn to use the badges by nearly filling each side of the meter before leaving. If the bros. cannot completely fill the meter, she comes back and fills the meter for them.
Names in other languages