The growing demand for nutritionally enriched and sustainable meat products has stimulated interest in the utilization of edible animal by-products and plant-based ingredients. The present study aimed to develop lamb pâté formulations containing lamb liver, lamb heart, mung bean, and chickpea and to evaluate their physicochemical, functional–technological, nutritional, microbiological, and contaminant characteristics. Four formulations were prepared, including a control without lamb offal and three experimental formulations containing 13%, 15%, and 17% lamb offal. Mung bean and chickpea were maintained at fixed levels of 7.5% each in all formulations; therefore, the experimental design primarily evaluated the replacement of lean lamb meat with increasing proportions of liver and heart. The effects of lamb offal incorporation on proximate composition, water-holding capacity, water-retention capacity, sensory characteristics, amino acid composition, vitamin and mineral composition, microbiological quality, and heavy metal content were investigated. Among the formulations evaluated, O-2 containing 15% lamb offal showed a favorable combination of physicochemical, water-binding, and sensory characteristics, including a protein content of 26.0%, fat content of 24.9%, moisture content of 62.5%, and the highest water-holding capacity (70.0%). O-2 also received the highest numerical sensory scores, although these were not significantly different from O-1 for several sensory attributes. Amino acid analysis confirmed the presence of essential and non-essential amino acids in the selected O-2 formulation. Compared with the control, O-2 showed numerically higher concentrations of the investigated B-group vitamins and significantly higher concentrations of iron, calcium, and potassium. At the investigated time point, O-2 showed a low total viable count (2.1 × 10² CFU/g), no detectable pathogenic microorganisms, and compliance with the evaluated microbiological criteria; lead and mercury were not detected under the analytical conditions used. Overall, the results indicate that partial replacement of lean lamb meat with edible lamb liver and heart within the fixed pulse-containing formulation can provide pâté with favorable physicochemical, water-binding, sensory, and nutritional characteristics. Further storage studies are required to establish shelf-life stability and microbiological safety throughout storage.