It is an old-fashioned word. You will find it in older books. You may find it when someone is trying to sound old fashioned--when playing a fantasy role-playing game, perhaps. Here are some examples of use. Know what the word means, but don't use it unless there is some special reason.
It is a dignified way to say "for fear of." It refers to something that is being done, in order to stop something bad from happening.
J. R. R. Tolkien, "The Lord of the Rings," intentionally written in an old-fashioned style: "Gollum went to guard the entrance, lest the 'thief' should escape." He was afraid the thief would escape, so he guarded the entrance to prevent that.
"Lest We Forget: The Passage from Africa to Slavery and Emancipation." This is a book title. The author was afraid this story would be forgotten, so she wrote this book to prevent the story from being forgotten.
Emily Dickinson (1830-1866)
"The maple wears a gayer scarf,
The field a scarlet gown.
Lest I should be old-fashioned,
I'll put a trinket on."
She was afraid people would think she looked old-fashioned, so she decided to put some pretty jewelry on.