I have always thought that lateral load is horizontal and not vertical in direction. For example, from this MIT notes and many others:
The lateral load resisting systems for earthquake loads are similar to those for wind loads. Both are designed as if they are horizontally applied to the structural system.
But the textbook I have (Mechanics of materials, 7th edition, Gere and Goodno, page 412) shows a vertical load on a beam and says it is lateral load. Here is the page:
Is there a convention for loading directions and the authors happens to use different one or should not Q above be called transverse load?