Mantle xenoliths in Pliocene alkali basalts of the eastern Betics (SE Iberia, Spain) are spinel ± plagioclase lherzolite, with minor harzburgite and wehrlite, displaying porphyroclastic or equigranular textures. Equigranular peridotites have olivine crystal preferred orientation (CPO) patterns similar to those of porphyroclastic xenoliths but slightly more dispersed. Olivine CPO shows [100]‐fiber patterns characterized by strong alignment of [100]‐axes subparallel to the stretching lineation and a girdle distribution of [010]‐axes normal to it. This pattern is consistent with simple shear or transtensional deformation accommodated by dislocation creep. One xenolith provides evidence for synkinematic reactive percolation of subduction‐related Si‐rich melts/fluids that resulted in oriented crystallization of orthopyroxene. Despite a seemingly undeformed microstructure, the CPO in orthopyroxenite veins in composite xenoliths is identical to those of pyroxenes in the host peridotite, suggesting late‐kinematic crystallization. Based on these observations, we propose that the annealing producing the equigranular microstructures was triggered by melt percolation in the shallow subcontinental lithospheric mantle coeval to the late Neogene formation of veins in composite xenoliths. Calculated seismic properties are characterized by fast propagation of P waves and polarization of fast S waves parallel to olivine [100]‐axis (stretching lineation). These data are compatible with present‐day seismic anisotropy observations in SE Iberia if the foliations in the lithospheric mantle are steeply dipping and lineations are subhorizontal with ENE strike, implying dominantly horizontal mantle flow in the ENE‐WSW direction within vertical planes, that is, subparallel to the paleo‐Iberian margin. The measured anisotropy could thus reflect a lithospheric fabric due to strike‐slip deformation in the late Miocene in the context of WSW tearing of the subducted south Iberian margin lithosphere.