"The fear made me unable to sleep."
Translation:Strach spowodował, że nie mogłam spać.
Wikipedia says that "lęk" is internal, it's a state of anxiety that may not even be caused by anything specific, a sense that something bad is coming. "strach" should be caused by a specific danger.
I don't feel like this is something that people who aren't interested in psychology are able to tell apart. I think that we can safely accept it.