According to the arrest affidavit a criminal history of Alissa shows only a charge for third degree assault out of Arvada in 2018. I don't think that's a felony charge.
Under federal law, people are generally prohibited from purchasing or possessing firearms if they have been convicted of a felony or some domestic violence misdemeanors, or if they are subject to certain court orders related to domestic violence or a serious mental condition. However, federal law merely provides a floor, and has notable gaps that allow individuals who have demonstrated significant risk factors for violence or self-harm to legally acquire and possess guns.
It appears his family never made him seek diagnosis and treatment, even though he exhibited symptoms of mental illness while in high school.