which is to say, real numbers that one can obtain by adding or subtracting other real numbers.
 which is a set that satisfies addition, commution, and inversion to derive any element from some subgroup of the set. Integers are an example, as one can produce any integer as a combination of the number 1.
The way lattice math has intruded into my outgroup awareness is from C Gentry's formulation of a fully homomorphic encryption scheme using lattices. So, if you are interested in a survey of papers delving into the applications of lattices for cryptography, consider looking at this 70 page work. I guess if you want to see some code that results from understanding this stuff, consider looking over Shai Halevi's HELib repo: https://github.com/shaih/HElib
A simple example is Z², this is the set of all pairs of integers (a,b) where addition is defined as (a,b)+(c,d)=(a+c,b+d).
A more interesting example is the set of pairs (a,b√2) where a and b are integers and addition is defined as (a,b√2)+(c,d√2)=(a+c,(b+d)√2).
If you draw those in R² they look like repeating parallelograms (squares actually for the first), hence lattices