If you cut down on the nuts, you'll cut out some fat. If you dilute your whole eggs with egg whites (in a carton in the dairy case is where you'll find them), you'll cut down on fat from the eggs.
That's not to say you have to lose those two foods, entirely. And that's not to say they don't have good nutrients, but they will definitely add fat, which means adding calories. More than carbs or lean protein.
The lean mass is, I assume, muscle, and you keep that by exercising (resistance training strengthens muscles, giving you lots of flexibility when you exercise to work on different muscles). Fat mass is going to go when you lose weight while maintaining lean mass with activity.