The restraining measures due to the COVID-19 outbreak deeply affected the general population’s sleep health and psychological status. The current literature proposes young and older people as two particularly at-risk groups. However, the differential impact of the lockdown period in these specific age categories needs to be disentangled. Through a web-based survey adopting validated questionnaires, we evaluated and compared sleep quality/habits, insomnia, perceived stress, depression, and anxiety symptoms of Italian late adolescents (n = 670; mean age ± SD, 19.38 ± 0.74, 18–20 years) and elderly (n = 253; 68.18 ± 2.79, 65–75 years). Young respondents reported more severe insomnia symptoms, worse subjective sleep quality, longer sleep latency, higher daytime dysfunction, and a more prevalent disruption of sleep habits (bedtime, get-up time, nap) than the elderly. On the other hand, older participants showed shorter sleep duration, lower habitual sleep efficiency, and greater use of sleep medications. Finally, the younger population displayed higher levels of depression and perceived stress. Our findings indicate that the lockdown period had more pervasive repercussions on sleep and the mental health of late adolescents. The implementation of supportive strategies is encouraged for this vulnerable population group.