Diagonally dominant lattices have already been used in cryptography, notably in the GGH and DRS schemes. This paper further studies the possibility of using diagonally dominant matrices in the context of lattice-based cryptography. To this end we study geometrical and algorithmic properties of lattices generated by such matrices. We prove novel bounds for the first minimum and the covering radius with respect to the max norm and study the quality reached by a specific solver for the Approximate Closest Vector Problem. Using these new results, we propose an decryption failure free encryption scheme using diagonally dominant matrices. We then propose solutions to patch the DRS signature scheme, in particular using matrices with negative noise.