There seem to be several plausible explanations for the name Laurie in the song Laurie (Strange Things Happen), performed by Dickie Lee but written by songwriter Mitt Addington.
1) Laurie Wilkins
The song was released as a A-side album along with "The Girl from Peyton Place" a song which shares a title (and publishing year) with the book of the same name written by George Melitalious. In the book, it is repeatedly stressed that Laurie Wilkens, a reporter for the Laconia Evening Citizen had helped Grace Metalious to write Peyton Place and was invaluable because of her knowledge of "local lore and mysteries".
Mitt Addington had to have heard the origin story somewhere and assuming that there was some connection between Mitt Addington and Laurie Wilkins, the name Laurie may have been chosen to replace the original name from the story on which the song is based; "Resurrection Mary" which record producers would have been loathe to use for religious reasons.
2) Laurie Allen
Mitt Addington was great friends with Laurie Allen (of Bobby and Laurie fame). It's possible that as he was writing songs for them at the time he wrote Strange Things Happen, he simply selected the name as a tribute to their friendship.