The hole-doped kagome lattice of Cu2+ ions in LaCuO2.66 was investigated by nuclear quadrupole resonance (NQR), electron spin resonance (ESR), electrical resistivity, bulk magnetization and specific heat measurements. For temperatures above ~180 K, the spin and charge properties show an activated behavior suggestive of a narrow-gap semiconductor. At lower temperatures, the results indicate an insulating ground state which may or may not be charge ordered. While the frustrated spins in remaining patches of the original kagome lattice might not be directly detected here, the observation of coexisting non-magnetic sites, free spins and frozen moments reveals an intrinsically inhomogeneous magnetism. Numerical simulations of a 1/3-diluted kagome lattice rationalize this magnetic state in terms of a heterogeneous distribution of cluster sizes and morphologies near the site-percolation threshold.
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