Conditional custom menu?

I do not believe a plugin would be needed for this.

You could add a class to the menu item (enable the class field under Screen Options when you are editing the menu item). Also be sure that you have the body_class() function applied to your body tag. Then you can do:

.your-menu-item-class {
    display: none;
}
.logged-in .your-menu-item-class {
    display: block;
}