In the present work, we consider the existence and spectral stability of multi-pulse solutions in Hamiltonian lattice systems. We provide a general framework for the study of such wave patterns based on a discrete analogue of Lin's method, previously used in the continuum realm. We develop explicit conditions for the existence of m-pulse structures and subsequently develop a reduced matrix allowing us to address their spectral stability. As a prototypical example for the manifestation of the details of the formulation, we consider the discrete nonlinear Schrödinger equation. Different families of 2-and 3-pulse solitary waves are discussed, and analytical expressions for the corresponding stability eigenvalues are obtained which are in very good agreement with numerical results.

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