The mnemonic I use is that longitude lines are all equally long, which means they must be the one that are meridians and thus go north-south.

In contrast, latitude lines are all different lengths, analogous to how being given latitude in the figurative sense affords you freedom of choice.

(I’m willing to bet there’s an Age of Exploration sailing idiom somewhere in that etymology, BTW – probably something about how straying north or south of your target course in order to catch the right wind is no big deal because you can just use your sextant to keep track of it, but straying farther east or west than you intend means you’re screwed because chronometers hadn’t been invented yet.)