An excerpt about the moment when Lowery took the photo from The Bloody Battle for Suribachi by Richard Wheeler:

"Photographer Lou Lowery snapped the flag raising from a hole
where he crouched with BAR man Chick Robeson. Chick had been
urged to join the flag-raising group for the picture but had refused,
insisting that he was no “Hollywood Marine.” In addition to the
four flag raisers—Schrier, Thomas, Hansen and Lindberg—also
identifiable on the photo is Pfc. James R. Michels, the man on
guard in the foreground.

Though most of our men were aware of the significance of their
accomplishment, no one at first did much thinking in terms of pride
and glory. All were concerned about the effect the sight of the colors
would have on the enemy. They were in danger of getting resistance
not only from the Japanese close at hand but from artillery units in
the north. The forty men had raised the flag, but they were by no
means certain they would be able to defend it successfully.
Shells from the north wouldn’t come until later, but the flag was
promptly challenged by the Japanese on the summit. First a rifleman
stepped out of a cave and fired at the photographer and Chick
Robeson. The Japanese missed, but Robeson didn’t. He swung his
BAR up for a long burst, and the man dropped heavily.
“You got him!” Harold Schrier said..." - The Bloody Battle for Suribachi by Richard Wheeler page 132-133

An excerpt from INVESTIGATING IWO: The Flag Raisings in Myth, Memory, & Esprit de Corps, Contributing editorBreanne Robertson, PhD:

"According to Marine cinematographer
Norman T. Hatch, who was also the photographic
officer (Warrant Officer) in charge of
the 5th Marine Division Photographic Section,
Lowery’s film was sent “out with the press boat
that night, but he did not learn for about 10
days if his film had survived.” Lowery feared
his film had been damaged, since just after he
photographed the first flag raising, he jumped
to escape a grenade, damaging one of his cameras.
Hatch also described how, after the film
was processed and cleared by censors, “Rosenthal’s
photo was sent by ‘wirephoto’ to the
United States, and Lowery’s photos of the ascent
and first flag raising were sent by air to
the Division of Public Relations, Headquarters,
U.S. Marine Corps.”" - https://www.usmcu.edu/portals/218/investigating%20iwo_web2.pdf page 47-48 (76-77 in pdf)

Wikipedia description of the photo, including who is in it and identifiers in the photograph.

"Raising the First Flag on Iwo Jima by SSgt. Louis R. Lowery, USMC, is the most widely circulated photograph of the first flag flown on Mt. Suribachi

Left to right: 1st Lt. Harold Schrier (kneeling behind radioman's legs), Pfc. Raymond Jacobs (radioman reassigned from F Company), Sgt. Henry "Hank" Hansen wearing cap, holding flagstaff with left hand), Platoon Sgt. Ernest "Boots" Thomas (seated), Pvt. Phil Ward (holding lower flagstaff with his right hand), PhM2c. John Bradley, USN (holding flagstaff with both hands, his right hand above Ward's right hand and his left hand below.), Pfc. James Michels (holding M1 Carbine), and Cpl. Charles W. Lindberg (standing above Michels)." - https://en.wikipedia.org/wiki/Raising_the_Flag_on_Iwo_Jima#/media/File:First_Iwo_Jima_Flag_Raising.jpg