The outbreak of the novel Coronavirus in late 2019 brought severe devastation to the world. The pandemic spread across the globe, infecting more than ten million people and disrupting several businesses. Although social distancing and the use of protective masks were suggested all over the world, the cases seem to rise, which led to worldwide lockdown in different phases. The rampant escalation in the number of cases, the global effects, and the lockdown may have a severe effect on the psychology of people. The emergency protocols implemented by the authorities also lead to increased use in the number of multimedia devices. Excessive use of such devices may also contribute to psychological disorders. Hence, hence it is necessary to analyze the state of mind of people during the lockdown. In this paper, we perform a sentiment analysis of Twitter data during the pandemic lockdown, i.e., two weeks and four weeks after the lockdown was imposed. Investigating the sentiments of people in the form of positive, negative, and neutral tweets would assist us in determining how people are dealing with the pandemic and its effects on a psychological level. Our study shows that the lockdown witnessed more number positive tweets globally on multiple datasets. This is indicative of the positivity and optimism based on the sentiments and psychology of Twitter users worldwide. The study will be effective in determining people's mental well-being and will also be useful in devising appropriate lockdown strategies and crisis management in the future.