An evil spirit from the Lord, means trouble of mind, and/or of body:
An evil spirit troubling the mind: Besides the mentioned King Saul, King David was after the adultery/murder incident also troubled by an evil spirit. While King Saul persisted in his rebellion against God, King David humbled himself and eventually found solace.
Psalm 6 (KJ21) David: "O Lord, rebuke me not in Thine anger, neither chasten me in Thy hot displeasure. Have mercy upon me, O Lord, for I am weak; O Lord, heal me, for my bones are vexed. My soul is also sore vexed, but Thou, O Lord, how long? Return, O Lord, deliver my soul! O save me for Thy mercies’ sake".
An evil spirit troubling the body: The apostle Paul suffered from the workings of an evil spirit. He had asked God to remove this spirit, but got the answer that: "My grace is sufficient for you".
2 Cor 12:7-10 (NIV) "... in order to keep me from becoming conceited, I was given a thorn in my flesh, a messenger of Satan, to torment me. Three times I pleaded with the Lord to take it away from me. But he said to me, “My grace is sufficient for you, for my power is made perfect in weakness.” Therefore I will boast all the more gladly about my weaknesses, so that Christ’s power may rest on me. That is why, for Christ’s sake, I delight in weaknesses, in insults, in hardships, in persecutions, in difficulties. For when I am weak, then I am strong".
An evil spirit troubling both the mind and the body: Job was driven to near insanity when an evil spirit from the Lord destroyed both his family and his health.