Background: Changes in lifestyle, finances and work status during COVID-19 lockdowns may have led to biopsychosocial changes in people with pre-existing vulnerabilities such as Major Depressive Disorders (MDDs) and Multiple Sclerosis (MS). Methods: Data were collected as a part of the RADAR-CNS (Remote Assessment of Disease and Relapse—Central Nervous System) program. We analyzed the following data from long-term participants in a decentralized multinational study: symptoms of depression, heart rate (HR) during the day and night; social activity; sedentary state, steps and physical activity of varying intensity. Linear mixed-effects regression analyses with repeated measures were fitted to assess the changes among three time periods (pre, during and post-lockdown) across the groups, adjusting for depression severity before the pandemic and gender. Results: Participants with MDDs (N = 255) and MS (N = 214) were included in the analyses. Overall, depressive symptoms remained stable across the three periods in both groups. A lower mean HR and HR variation were observed between pre and during lockdown during the day for MDDs and during the night for MS. HR variation during rest periods also decreased between pre- and post-lockdown in both clinical conditions. We observed a reduction in physical activity for MDDs and MS upon the introduction of lockdowns. The group with MDDs exhibited a net increase in social interaction via social network apps over the three periods. Conclusions: Behavioral responses to the lockdown measured by social activity, physical activity and HR may reflect changes in stress in people with MDDs and MS. Remote technology monitoring might promptly activate an early warning of physical and social alterations in these stressful situations. Future studies must explore how stress does or does not impact depression severity.