In the last decade, several studies have reported enrichments of the heavy isotopes of moderately volatile elements in lunar mare basalts. However, the mechanisms controlling the isotope fractionation are still debated and may differ for elements with variable geochemical behaviour. Here, we present a new comprehensive dataset of mass-dependent copper isotope compositions (delta 65Cu) of 30 mare basalts sampled during the Apollo missions. The new delta 65Cu data range from +0.14 %o to +1.28 %o (with the exception of two samples at 0.01 %o and -1.42 %o), significantly heavier than chondrites and the bulk silicate Earth. A comparison with mass fractions of major and trace elements and thermodynamic constraints reveals that Cu isotopic variations within different mare basalt suites are mostly unrelated to fractional crystallisation of silicates or oxides and late-stage magmatic degassing. Instead, we propose that the delta 65Cu average of each suite is representative of the composition of its respective mantle source. The observed differences across geographically and temporally distinct mare basalt suites, suggest that this variation relates to large-scale processes that formed isotopically distinct mantle sources. Based on a Cu isotope fractionation model during metal melt saturation in crystal mush zones of the lunar magma ocean, we propose that distinct delta 65Cu compositions and Cu abundances of mare basalt mantle sources reflect local metal melt-silicate melt equilibration and trapping of metal in mantle cumulates during lunar magma ocean solidification. Differences in delta 65Cu and mass fractions and ratios of siderophile elements between low- and high-Ti mare basalt sources reflect the evolving compositions of both metal and silicate melt during the late cooling stages of the lunar magma ocean.