Because I'm thinking of a certain spatial orientation, consider an example at hand. You are sitting at your keyboard which is flat on your desk. The keys ASDFJKL are arranged laterally, whereas the keys MKI8 are arranged [word goes here].
"Longitudinally" in this context becomes confusing, because it appears to mean the same direction as "laterally". "Laterally" seems most apt as I've used it, because it's used in regards to the orientation of the object (side to side). "Longitudinally" appears apt only because of the aspect ratio of the object (along the long dimension).
Anatomical terms and simple antonyms such as "medially" seem to suggest a location more so than a direction. Other suggested antonyms like "perpendicularly" or "crosswise" are ambiguous.