There are two ways to interpret this verse:
If Saul does not know the Lord this could be perceived as an demonic spirit that entered Saul at the allowance of the Lord. This would be similar to the case of Job. Of course, we've seen that Saul has disobeyed the Lord and that (if he doesn't know the Lord) he might be open to an attack of Satan.
The second theory is that this spirit is not demonic, but a spirit of conviction for his sin. We know that when we, as Christians, disobey our father he chastises us & often that includes conviction of the Holy Spirit.
I believe that Saul knew the Lord. I believe this because of many tiny clues I read along the way and one great big neon sign in chapter 28.
Let me give you a little background if you are unfamiliar with the story:
The Philistines were gathering and Saul began to worry so he instructed his servants to seek out a woman with a "familiar spirit." When the woman was found, Saul disguised himself and went to her. She was concerned at first because Saul had killed any one practicing witchcraft, but Saul assured her that she would suffer no punishment, and asked her to bring up Samuel.
The familiar screamed because she succeeded in bringing up Samuel and was told that she was face to face with her greatest fear, the King Saul. What Samuel said to Saul is my neon sign:
Now, I don't know about you, but I think this is very clear. When Saul died he was going to be where Samuel is, as would Jonathan. If Saul was not saved, neither was Samuel or Jonathan.