Holographic lenses allow the spatial storage of the phase profile of a desired wavefield distribution into monolithic elements composed of multiple variable cells. This process of wavefield encoding into a lens is helping to create tools for all sorts of wavefield manipulation needs, including beamforming and imaging. In acoustics, and ultrasounds more specifically, many applications can benefit from such versatility as ultrasonic sources are by nature highly directive. Examples of wave collimation or focusing are highly sought after for non-invasive biomedical applications. Imprinting the wavefront information is generally conducted in either transmission or reflection applications, such as for custom transmitted acoustic energy manipulation or for the control of the reflected wavefields. However, simultaneous control of both reflected and transmitted fields has not yet been fully investigated for ultrasound applications despite the numerous applications in optics. In this work, we present the case of a bi-directional non-mirror symmetric ultrasonic lens that works simultaneously in transmission and reflection, allowing to control the spatial phase distribution in both directions. We report a lens behaving as a bi-directional Lambertian scatterer, i.e., the reflected and transmitted fields exhibit an omnidirectional scattering pattern, a simple scenario from which other reflected/transmitted wavefields can be explored further along.