  In this paper we show how to lift Lagrangian immersions in $\mathbb{C}
P^{n-1}$ to produce Lagrangian cones in $\mathbb{C} ^n$, and use this process
to produce several families of examples of Lagrangian cones and special
Lagrangian cones. Moreover we show how to produce Lagrangian cones, isotopic to
the Harvey-Lawson and trivial cones, whose projections to $\mathbb{C} P^{n-1}$
are immersions with few transverse double points.
