This claim is true and can be backed by research. According to the National Library of Medicine, an online library filled with factual journal articles, sleep deprivation in adolescents is correlated with mental health issues in young adults. The research provided proves this claim and provides logical evidence to support the LA Times article.
Excerpt: " In fact, insomnia in the general teenage population is associated with mental health difficulties later in life and increased risk of interpersonal problems and psychiatric disturbances, which may include mood and anxiety disorders, risk-taking behaviors, substance use disorders, and higher suicidal risk [15,16,17]"
Article: https://pmc.ncbi.nlm.nih.gov/articles/PMC10136689/#:~:text=In%20fact%2C%20insomnia%20in%20the,15%2C16%2C17%5D.