This question is really too broad, given the ubiquity of lattices in Mathematics. Just to have an idea, you can google "Lattices and $x$", where $x$ is one the following (huge) subjects:

• Sphere packings
• Geometry of numbers
• Complex abelian varieties
• Locally homogeneous manifolds
• Criptography and digital communication via algebraic codes (for instance, Golay code).