you have to increase the divisions of your lattice. in the channelBox look under SHAPES of your ffd1LatticeShape. there you can change the S, T and U divisions.
to deform a plane into a shape of a cylinder I´d rather use one of the non-linear deformers like Bend. you have to place the deformer (rotation/translation) to get the desired effect.
everything starts and ends in the right place at the right time.