Doug Solomon — the 26-year-old Manhattanite who, police say, bashed his mother to death with a lamp on Tuesday before jumping out a window to his own death — is remembered as being withdrawn and at loose ends.

“He displayed a lot of signs of depression,” a former classmate from the elite Poly Prep Country Day School in Brooklyn told The Post. “He was not going out to clubs or doing much of anything. He was anti-social. I didn’t reach out to Doug but, after talking to some people from our Poly Prep friend group, it sounded like he didn’t want to be reached out to. You don’t want to ask what’s going on to a person who has nothing going on.”

Police sources described the son of retired New York Justice Charles Solomon as “rudderless.” A background check on Doug, who still lived at home with his parents, nearly eight years after dropping out of Rhodes College during his 2014-2015 freshman year, shows no history of employment.

The former classmate added, “We all loved Doug. But if he was still alive, and if we hit him up right now, he would probably be chilling in his room.”

Doug played on the Poly Prep lacrosse team, and the classmate remembers him as being “off brand. Doug would be on the red top [school basketball court] shooting baskets in the style of different NBA players. He amused people. In lacrosse, he was crafty and skilled. He had the whole look: the crazy flow, the lettuce [slang for long hair] in the back of his helmet. Doug flowed like the Mississippi. He had swagger on the field. That was his comfort zone. He was a naturally talented athlete but he did not push himself to the degree that he could have. He lacked drive.”

This was especially unusual at Poly, a pricy Bay Ridge academy (12th-grade tuition for 2022-2023 runs $57,870) loaded with overachievers who, according to one staffer, often go on to attend top universities.

The staffer recalled how Doug made captain of the team during his senior year, but was still a chronic underachiever. “Hewas the most unmotivated,” the staffer said, explaining that, at 6 feet 1 and 175 pounds, the teen had all the natural attributes for superstardom on the field. “He was a big kid and a lefty — which is usually good combination for scoring — but he just didn’t work hard even though it looked like he had talent. It was disappointing.”

He also described Solomon as an introvert to the point where “it was weird.” If questioned about a play, “he wouldn’t even answer.”

According to law enforcement sources, Doug — who was naked when he apparently jumped from the family’s luxury 16th-floor apartment on East 79th Street, in a building where a three-bedroom unit recently hit the market for $2,450,000, and was heard screaming on the way down — had a proclivity for heavy drinking and pot smoking. “I wouldn’t be surprised,” said the staffer.

Perhaps most shocking for those who knew Doug is that he would murder his mother, 65-year-old Diane Gallagher, who taught dance at PS 190 in East New York, Brooklyn, and directed the high school musical at the Upper East Side’s PS 183.

By all indications, at least during his high school years, they got along well. “We would hang out at the apartment on East 79th Street. Doug was awesome back then. His parents were cool to be around. His mom was uplifting,” the former classmate recalled. “She’d ask questions about your life and always offer food and beverages and be very attentive and really nice to us, always smiling. It was a great situation there. They were a great family. It’s hard to imagine where [the brutal murder of his mother] would come from. It doesn’t seem real. It really doesn’t.”

“I remember her having an adoring relationship with her son,” a friend of Diane’s told The Post. “She was so proud of him graduating and getting into college. She spoke about him effusively and seemed to adore him.”

But things did not go as planned at Rhodes and life began to slide downhill for Doug. If he was stoked to play on the lacrosse team, you’d never know it. The coach there does not remember him showing up for preliminary practices and he is not listed on the team roster for the 2014 season.

“He was part of a fraternity at college,” remembered the former classmate. “It looked like he was partying and whatnot.”

Indeed, a 2014 photo on Facebook shows Doug with a cigarette or joint dangling out of his mouth and a haze of smoke in front of his face.

He dropped out of college before completing his freshman year, moved back home, and apparently never quite got it together. He saw a therapist for a while after leaving college.

“Doug could have had mental blocks in his head that slowed him down. Maybe he had a learning disability,” said the former classmate. “I can tell you that he lacked confidence and did not want to be studious. College was not right for him.”

His sister, Leah Solomon, 28, graduated from the University of Pennsylvania with a bachelor’s degree in economics. She works as an acquisitions associate for an investment firm and lives in the Kips Bay neighborhood.

Meanwhile, according to police sources, Doug deteriorated into a rage-fueled layabout who spent his time smoking pot and drinking alcohol. Father Charles told authorities that there had been no history of domestic issues, though he and his now-deceased wife are said to have had discussions the night before about what to do with their son.

As the friend told The Post, last time she ran into Diane, just three months ago, “She had a big smile on her face. She seemed the same as always … She seemed to have an idyllic life. No one knows what goes on between the walls of [another family’s] apartment, but she never seemed less than lovely.”

However, on the morning of the apparent murder-suicide, a resident who lives a few floors below the Solomons reportedly heard shouting .

“Something snapped inside of Doug,” the former classmate believes. “It must have been a 30-second lapse of judgment and his life changed. I can’t believe that any of it was premeditated. He sees his mother unconscious and can’t live with himself. He didn’t want to rot away for 30 years in jail. He was such a nice kid. Now, to be remembered for this, is awful.”