The reasoning that COVID-19 elevates the levels in the body of Cathepsin-L (CTSL), which raises cancer risk as well as increases the rate at which tumors develop, is proved with scientific support to some extent, but not by conclusive scientific proof. Well, SARS-CoV-2, which is the originator of COVID-19, has been cited as upregulating CTSL in human cells. Evidence indicates that CTSL is part of the mechanism through which viruses enter the cell and over-expressed in the most critically ill patients with COVID-19 (source). However, while CTSL plays a role in the process of cancer development, most specifically to metastasize and destabilize tissue barriers, it has been theorized, though not yet directly shown, that COVID-19 infection can be a direct cause for cancer development through upregulation of CTSL. The relationship between CTSL and cancer is complex, with elevated levels of CTSL predicting poor prognosis in various cancers, such as breast and lung cancer (source). Yet, no definitive studies have proven that COVID-19 infection hastens cancer risk by increasing levels of CTSL. Therefore, while there is some rationale behind the claim due to SARS-CoV-2 upregulating CTSL and its contribution towards cancer promotion, the reality is that there still is no clear justification to presume COVID-19 leads to cancer risk in this way directly (source).
Sources:
Nature.com – Research on SARS-CoV-2’s effect on CTSL: Link
Frontiersin.org – Article on CTSL’s role in cancer: Link
Biomarker Res. – Study on CTSL and cancer progression: Link