"There's obviously multiple outcomes of an investigation," Horsley said, "and we'll take appropriate action at that time.
Lyman has hired local defense attorney Ed Brass, who was unavailable for comment late Thursday night.
When reached by telephone Thursday, Cottonwood quarterback Cooper Bateman said he was stunned by the allegations and that he had not been informed that Lyman was facing possible dismissal.
"You'd never think of Josh and that," Bateman said. "He's professional in everything he does, and I'd never expect him to do anything like that."
One Cottonwood assistant coach, who asked not to be named, said members of Lyman's staff have been instructed not to contact the coach until after the school year. Horsley said only that the district advises employees not to contact a subject until an investigation concludes.
As a player, Lyman won three championships at Skyline High School and went on to become a receiver at the University of Utah from 1999 to 2001. He was named honorable mention All-Mountain West Conference as a senior.
"Hopefully it's not as bad it looks," said former Skyline coach Roger Dupaix, who retired in January as the winningest coach in state history. He remembered Lyman as an "All-American young man" who had adjusted well to unexpectedly becoming a varsity head coach.
Lyman was hired as Cottonwood's interim head coach in 2010 after Teko Johnson, who had been hired as coach that summer, died of a heart attack in Atlantic City, N.J.
He guided the Colts to an 10-1 record and the Class 5A quarterfinals. He was named The Tribune's coach of the year for his efforts.
Last season, the Colts finished 5-5. Cottonwood, known for producing Division I players such as Stanley Havili (USC) and Isi Sofele (California), is considered one of Class 5A's top teams next season and Bateman, who has offers from schools such as Alabama and LSU, is the state's top recruit.
Lyman was preparing for a high-profile year: The Colts are scheduled to host Skyline (Wash.) on Sept. 7 in a nationally televised game brokered by ESPN that will pit Bateman against Skyline's Max Browne, the top-rated quarterback in the country, who has committed to USC.
Horsley said the school had not yet appointed an interim head coach, saying that decision is "of little consequence at this point" and that the district's priority was "removing the alleged perpetrator from the classroom."
If the accusations against Lyman prove to be of a sexual nature, which Horsley would not confirm, it would be only the latest incident in history of alleged inappropriate contact between Utah teachers and students.
In 2009, there were 20,000 licensed teachers in Utah. According to a Tribune report from that year, the State Board of Education revoked 313 teacher licenses between 1992 and 2009, 208 for sexual misconduct. In 2005, Utah ranked 16th in the nation for teacher sex offenses, according to an Associated Press survey of disciplinary records from 2001 to 2005.
Tribune reporters Lisa Schencker, Kirsten Stewart and Janelle Stecklein contributed to this story.