It's counterintuitive because the prefix refers to the lines, but we're usually describing points along the lines. We know intuitively that "lateral" is side to side, and "long/length" we would expect to be vertical, but that describes where the lines sit, and the measurements are perpendicular to where the lines sit: you choose a horizontal line to describe a height(/length), and a vertical one to describe width.
So just remember that it's opposite to intuition, which will work until you've gotten comfortable enough that your intuition is correct and will then guide you exactly opposite.
I say longitude goes longways, which I know isn't accurate except fairly close to the poles, but I remembered it like that when I was a kid and it stuck.
I use Jimmy Buffet’s song “Changes in Latitude, Changes in Attitude”, meaning head south to Key West to change your attitude. Ergo, latitude is north/south.
So just remember that it's opposite to intuition, which will work until you've gotten comfortable enough that your intuition is correct and will then guide you exactly opposite.