The collision of the Indian and Asian plates since about 55 Ma has created the largest plateau with the thickest crust on Earth. There is, however, no general agreement on the modes of the crustal thickening. The crustal thickness of the Tibetan plateau still remains poorly determined. It is generally accepted that the Tibetan crust has roughly double normal thickness and that it thins somewhat toward the north, but individual observations of Moho depth vary spatially and for different techniques at the same place by greater than 20 km. In this work we compare P and S receiver functions at station LSA, located in the southern Lhasa terrane, to determine the crustal thickness beneath the station. A doublet Moho structure with two significant interfaces at about 60 and 80 km depth in the lower crust is seen clearly in the P receiver functions. The deeper phase (Moho) is, however, absent in the S receiver function data. Here we model the observed P and S receiver functions by a strong Moho topography that dips to the east at an angle of 30°. This result may indicate that the Moho structure beneath Tibet can be very complicated and has strong lateral variations and suggests that a detailed map of Moho depth is only possible with 2D dense seismic experiments. The Moho dips locally perpendicular to the direction of the Indian plate motion, suggesting that the lower crustal deformation is decoupled from the underlying Indian mantle lithosphere. The extremely strong Moho variation beneath and east of station LSA may also imply a crust-mantle interaction, specifically delamination or foundering of lower crust down to the upper mantle.