Stretching in Object When Subdividing Working on a project where it warps bottles using a lattice and curve. 
The original one I'm referencing (1st Image) is what I'm trying to recreate. As you can see when a subdivision is applied it smooths out very well.

However with the one that i'm working on (2nd Image) when I add the subdivision modifier it does not smooth out, instead it looks stretched and creates vertical lines.
It looks to me in that tiny picture that your object is triangulated, and if so then you will definitely get artifacts when bending and stretching. If you can test your lattice and curve setup on a similar form made of entirely quadrilaterals, see if that doesn't fix the issue with the stretching.