If you do something lest something unpleasant should happen, you do it to try to prevent the unpleasant thing from happening. [formal]
I was afraid to open the door lest he should follow me.
The president has gone along with the hardliners lest they be tempted to oust him.
And, lest we forget, Einstein wrote his most influential papers while working as a clerk.
Synonyms: in case, in order to avoid, for fear that, in order to prevent