What is lateral transmission?

It is the phenomenon of sound passing around a sound proofing partition, mostly through the building structure.
It is called also 'flanking transmission'.
For example when you build a sound insulating counter-wall to increase an existing wall sound insulating power, it is often the sound passing through the ceiling, the floor and the other walls as a vibration that decreases actual sound insulation.
This is why the only guarantee in sound insulating existing rooms for music purposes is to apply insulations on all of its surfaces, possibly detached via elastic media from the existing ones: this is the ‘box within the box’ concept.
Structural transmission is easily noticed in concrete built buildings, where you can even hear footsteps or other noises that don’t come from the closer neighbours.