It may be too early to say that LSU had cut their coaching search to these four names, but according to SB Nation, these coaches are the leaders for the LSU head coaching job.
SB Nation cites multiple sources in the LSU program when it reports that Jimbo Fisher, Tom Herman, Jim Mora, and Dana Holgorsen as the most-favored candidates for the head coaching job, in that order.
Fisher and Herman have had their names tossed around the most for the job, so it's no surprise that those two top the list there. As for Mora and Holgorsen... those names are new, to say the least. Holgorsen has done a fine job at West Virginia, and Mora has done the same at UCLA. However, neither have set the world on fire with their performances, so it's interesting to see them so highly regarded for a job like LSU.
The SB Nation report also notes that current interim coach Ed Orgeron has a decent chance of keeping the job, and it might be guaranteed if the Tigers manage to beat Alabama this upcoming Saturday.
LSU is obviously in need of a full-time head coach after they fired Les Miles after a loss to Auburn in Week 3 of the season. LSU has consequently won all of their games under Orgeron.