We employ La-139 NMR spectroscopy as a structural probe of metallic La
2CuO4+delta. We find a distribution of lateral displacements of the ox
ygen atoms which form the apices of the oxygen octahedra. We directly
observe a wide distribution of structures of the La-O layer; this dist
ribution is strongly temperature dependent. We present copper NQR spec
tra which reveal a second, unexplained, copper site in the CuO2 planes
. We show that these features are not manifestations of disturbances o
f the lattice by interstitial dopants, but are the intrinsic response
of La2CuO4+delta to doped holes.