Water-based slurries with silica (SiO2) nanoparticles, graphene oxide (GO) nanosheets and GO/SiO2 hybrid nanostructures as abrasives were synthesised in order to achieve a high-efficiency and low-damage lapping. Tribological characteristics of SiO2, GO and GO/SiO2 nanoslurries were systematically investigated to optimise slurry formulae, and the lubricating mechanisms involved were revealed based on the analyses of worn surfaces and used slurries. Machining performance of the optimised slurries was then examined in the fixed abrasive lapping of glass substrates in terms of surface quality and material removal. The GO/SiO2 slurry of 0.16 wt.% at a mass ratio of 1:1 generated a lubricating layer consisting of C deposited and SiO2 dynamic films at the rubbing interface. This improved friction and wear conditions at the contact, producing a significantly lower COF and a better worn surface quality than those slurries containing only GO or SiO2. The lapping with the GO/SiO2 slurry thus reduced the surface damage on glass and achieved a crack-free subsurface. In comparison with a conventional lapping, the new lapping process resulted in a 35% reduction in surface roughness, but a 28% increase in material removal rate. Such improvements were attributed to the synergistic lubrication behaviour of the formed nanostructures of GO/SiO2 in water.