(1) Objectives: The COVID-19 pandemic has disproportionately affected the lives of older people. In this study, we examine changes in physical activity, sleep quality, and psychosocial variables among older people during COVID-19 lockdown. We build on cross-sectional studies on this topic by assessing change longitudinally. We also examined whether participant characteristics including demographic, cognitive, personality, and health variables were related to more positive or negative changes during lockdown. (2) Methods: 137 older participants (mean age 84 years) from the Lothian Birth Cohort 1936 study were included in the analysis. They completed the same questionnaires assessing physical activity, sleep quality, mental wellbeing, social support, loneliness, neighbourhood cohesion, and memory problems before (mostly 2 years earlier) and again during national lockdown. (3) Results: On average, levels of physical activity were reduced (those doing minimal physical activity increased from 10% to 19%) and perceived social support increased during lockdown (effect size drm = 0.178). More positive change in the psychosocial and behavioural outcome variables during lockdown was associated with personality traits (greater intellect, emotional stability, and extraversion) and having a higher general cognitive ability. Participants with a history of cardiovascular disease, more symptoms of anxiety, or who lived alone were more likely to experience negative changes in the outcome variables during lockdown. (4) Discussion: These results provide further insight into the experiences of older people during the COVID-19 pandemic and could help to identify those at greatest risk of negative psychosocial or behavioural changes during this time.