The COVID-19 pandemic's onset and the subsequent lockdowns drastically amplified digital interactions worldwide. These unparalleled shifts in online behavior birthed concerns about potential surges in cybersecurity threats, particularly cyberbullying. Our research aimed to explore these proposed trends on Twitter. Utilizing a dataset of 126,348 tweets from January 1st to September 12th, 2020, we honed in on 27 cyberbullying-related keywords, like 'online bullying' and 'cyberbullying'. Recognizing the limitations of traditional change-point models, we opted for a Generalized Additive Model (GAM) with spline-based smoothers. The results were revealing. A significant uptick in cyberbullying instances emerged starting mid-March, correlating with the global lockdown mandates. This consistent trend was evident across all our targeted keywords. To bolster our findings, we conducted lag-based assessments and compared the GAM against other modeling approaches. Our conclusions robustly indicate a strong association between the enforcement of pandemic lockdowns and a heightened prevalence of cyberbullying on Twitter. The implications are clear: global crises necessitate intensified cyber vigilance, and the digital realm's safety becomes even more paramount during such challenging times.