Background: On December 2019, an outbreak of atypical pneumonia, known as COVID-19, was identified in Wuhan, China. This disease, characterized by the rapid human-to-human transmission of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has spread rapidly in more than 200 countries. Northern Italy’s regions have been hit hard in terms of deaths. Here, we report the experience of the Pathology Department of the Fondazione IRCCS Istituto Nazionale Tumori (INT) in Milan, the first Italian public cancer center, in the period of the lockdown that took place in Lombardy from March to May 2020. Method: The variation in terms of exams was calculated in two different timeframes: December 2019–February 2020 (pre-COVID-19) and March–May 2020 (COVID-19). During these periods, Turn-Around-Time (TAT) metrics released by the Lombardy Region were calculated to assess if changes applied to guarantee the safeguarding of workers affected the average diagnosis time. Results: In the COVID-19 period, there was a decrease for all the performed exams. The most considerable decrease was observed for PAP tests (−81.6%), followed by biopsies (−48.8%), second opinions (−41.7%), and surgical (−31.5%), molecular (−29.4%) and cytological (−18.1%) tests. Measures applied within the Pathology Department, such as digital pathology, remote working, rotations and changes in operating procedures, improved the diagnostic performance as required by the guidelines of the Lombardy Region in terms of TAT. At the same time, the measures applied for the safeguarding of the personnel turned out to be feasible and did not affect the overall performance of the Pathology Department. Conclusions: The sharp slowdown in cancer screening during the first wave of COVID-19 could seriously endanger cancer prevention in the near future.