Sitting on the lotus means purity and no dye. With purity and non-staining, you can save all sentient beings with your fate, and let you stay away from the sea of suffering and go to the other side of nirvana. This is a metaphor for the immaculate body of Buddha.
The so-called "living without a fixed place" gives birth to a person's heart, does all good deeds, and does not live with others. This is an infinite use of the body. Although it plays an infinite role, it cannot be separated from the body.