Lean mass is everything but the fat. Fat mass only includes adipose tissue. Lean mass is like your house – it takes plumbing, electricity, lighting, running water, etc to make it comfortable, not to mention the amount of energy you pour into living your life that operates between its walls.
On the other hand adipose tissue cells are big storage units. The body’s systems are on the outside of those cells more like a storage unit. You don’t pay for heat, extra lighting, plumbing, etc to create a more comfortable space. It’s just a place to put your stuff. When you increase lean mass you need more energy to manage it.