The claim of Fleischmann and pons to have achieved "cold fusion" in a palladium crystal lattice saturated with lithium hydride (deuteride) has stimulated much discussion. Although they have an unexplained energy source, there exist no satisfactory fusion models that can account for their observations. We propose to study the quantum and statistical mechanics of various mechanisms for nuclear fusion in a palladium lattice. Our study takes into account the presence of both lithium and deuterium and provides an exhaustive and in-depth analysis of all paths that could lead to a cold fusion interpretation of the Fleischmann and pons experiment. The mechanisms to be studied include the direct fusion of deuterium nuclei, the fusion of a deuteron with a proton, the interaction of the lithium nucleus with a deuteron, the enhanced effective mass of an electron in a palladium lattice, and the stripping of a deuteron by a palladium nucleus.