Lachrymal things have something to do with tears or crying. Your dramatic friend's lachrymal outburst after you forgot her birthday probably included a lot of weeping and wailing.
When you spell lachrymal with a y, it tends to be literary or old-fashioned, like the lachrymal heroine of a nineteenth century novel. When it's spelled lachrimal, the meaning is usually more scientific, like the lachrimal gland in your eye, from which tears fall when you're sad or chopping onions. Lachrymal comes from the Greek dakryma, "tear," by way of the Latin lacrima, also "tear."