The influence of kinship on animal cooperation is often unclear. Cooperating Asiatic lion coalitions are linearly hierarchical; male partners appropriate resources disproportionately. To investigate how kinship affect coalitionary dynamics, we combined microsatellite based genetic inferences with long-term genealogical records to measure relatedness between coalition partners of free-ranging lions in Gir, India. Large coalitions had higher likelihood of having sibling partners, while pairs were primarily unrelated. Fitness computations incorporating genetic relatedness revealed that low-ranking males in large coalitions were typically related to the dominant males and had fitness indices higher than single males, contrary to the previous understanding of this system based on indices derived from behavioural metrics alone. This demonstrates the indirect benefits to (related) males in large coalitions. Dominant males were found to 'lose less' if they lost mating opportunities to related partners versus unrelated males. From observations on territorial conflicts we show that while unrelated males cooperate, kin-selected benefits are ultimately essential for the maintenance of large coalitions. Although large coalitions maximised fitness as a group, demographic parameters limited their prevalence by restricting kin availability. Such demographic and behavioural constraints condition two-male coalitions to be the most attainable compromise for Gir lions.