More generally, a lattice Γ in a Lie group G is a discrete subgroup, such that the quotient G/Γ is of finite measure, for the measure on it inherited from Haar measure on G (left-invariant, or right-invariant-the definition is independent of that choice).
A lattice is said to be uniform or cocompact if G/Γ is compact; otherwise the lattice is called non-uniform.