Diagonally dominant matrices have been a prolific object for mathematical studies for over a century; to this day, it is still an active topic of research. In this paper, we study the lattices generated by diagonal dominant matrices. First, we provide a novel upper bound on their shortest vectors in the maximum norm, as well as a novel bound on the covering radius. Furthermore, we provide a new lattice vector reduction algorithm that gives a better proven worst-case reduction in maximum norm than Babai's Round-Off algorithm within a polynomial amount of operations. Those results expand the understanding of this particular mathematical object, and have some potential applications in modular arithmetic, cryptography and cryptanalysis.