So below I summarised the main steps in how to deform a polygon using the lattice that surrounds it.
1. Increase the subdivisions on the polygon in the attribute editor
2. Click Deformation tab
3. Click Lattice
4. In the attribute editor click the Lattice Shape and increase the subdivisions
5. Select Lattice > right click > lattice point
NOTE: The more lattice subdivisions = less of the polygon to be affected
NOTE: Ctrl key can allow you to deselect
6. Edit > delete by type > history
NOTE: Lattice will then treat your deformed shape as an entirely new entity
Source : The CGBros. (2014). CGI 3D Tutorial HD: “Using Lattices in Maya” – by 3dmotive. Available: https://www.youtube.com/watch?v=jOq0H1V3mSE. Last accessed 10th Dec 2014.