It is a fairly "literary" word, used more in written English than spoken English, and more often in older writing.
I would define it as "so that you don't" or "in case."
It is often part of the colocation "lest we forget," which MIGHT be a reference to a famous poem by Rudyard Kipling, "Recessional."
I like to use Google News searches to find usage examples, because newspapers and journalism tend to be good contemporary English. I find plenty of examples of "lest." Here are a few of them:
Be on your guard, lest you find yourself on the receiving end of an April Fool’s Day prank.
(Describing a role-playing game) When the music ends, players must find a seat at a nearby region lest they fall under the influence of the various sea gods patrolling the floor.
Lest one suppose that five percent inflation is no big deal, look at the numbers leading up to August 15, 1971, when President Nixon slammed shut the gold window and ushered in the age of stagflation.