Lacustrine soils from the former Texcoco Lake within the Basin of Mexico, some 14 km north of Mexico City, have unique geotechnical properties. These materials have been thoroughly studied in the past, and yet, very few investigations have addressed the issue of the anisotropy of their shear stiffness modulus at very small strain levels (G0). Stiffness anisotropy, even at very small deformations, may significantly influence the response of the soil in a variety of cases and applications including soil-structure interaction problems under static and dynamic conditions. In this study, a large-size oedometer equipped with bender elements was used to measure the shear wave velocities along different paths as an indirect assessment of G0. The initial or inherent anisotropy of the materials was evaluated with these measurements. The experimental results revealed that the stress-induced anisotropy was not significant; hence, the shear stiffness modulus was seen to depend mainly on the initial anisotropy. An inverse correlation between the yield stress (σ’y) (or over-consolidation ratio, OCR) and the initial anisotropy was found, whereas a direct correlation between the liquidity index and the initial anisotropy was also disclosed.