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(1) Background: The aim of our study was to identify specific risk factors for fatal outcome in critically ill COVID-19 patients. (2) Methods: Our data set consisted of 840 patients enclosed in the LEOSS registry. Using lasso regression for variable selection, a multifactorial logistic regression model was fitted to the response variable survival. Specific risk factors and their odds ratios were derived. A nomogram was developed as a graphical representation of the model. (3) Results: 14 variables were identified as independent factors contributing to the risk of death for critically ill COVID-19 patients: age (OR 1.08, CI 1.06–1.10), cardiovascular disease (OR 1.64, CI 1.06–2.55), pulmonary disease (OR 1.87, CI 1.16–3.03), baseline Statin treatment (0.54, CI 0.33–0.87), oxygen saturation (unit = 1%, OR 0.94, CI 0.92–0.96), leukocytes (unit 1000/μL, OR 1.04, CI 1.01–1.07), lymphocytes (unit 100/μL, OR 0.96, CI 0.94–0.99), platelets (unit 100,000/μL, OR 0.70, CI 0.62–0.80), procalcitonin (unit ng/mL, OR 1.11, CI 1.05–1.18), kidney failure (OR 1.68, CI 1.05–2.70), congestive heart failure (OR 2.62, CI 1.11–6.21), severe liver failure (OR 4.93, CI 1.94–12.52), and a quick SOFA score of 3 (OR 1.78, CI 1.14–2.78). The nomogram graphically displays the importance of these 14 factors for mortality. (4) Conclusions: There are risk factors that are specific to the subpopulation of critically ill COVID-19 patients.