  We extract from a toric model of the Chekanov-Schlenk exotic torus in
$\mathbb{CP}^2$ methods of construction of Lagrangian submanifolds in toric
symplectic manifolds. These constructions allow for some control of the
monotonicity. We recover this way some known monotone Lagrangians in the toric
symplectic manifolds $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$
as well as new examples.
