Deviations in laboratory tests assessing liver function in patients with COVID-19 are frequently observed. Their importance and pathogenesis are still debated. In our retrospective study, we analyzed liver-related parameters: aspartate aminotransferase (AST), alanine aminotransferase (ALT), alkaline phosphatase (ALP), gamma-glutamyltransferase (GGT), total bilirubin (TBIL), albumin, comorbidities and other selected potential risk factors in patients admitted with SARS-CoV-2 infection to assess their prognostic value for intensive care unit admission, mechanical ventilation necessity and mortality. We compared the prognostic effectiveness of these parameters separately and in pairs to the neutrophil-to-lymphocyte ratio (NLR) as an independent risk factor of in-hospital mortality, using the Akaike Information Criterion (AIC). Data were collected from 2109 included patients. We created models using a sample with complete laboratory tests n = 401 and then applied them to the whole studied group excluding patients with missing singular variables. We estimated that albumin may be a better predictor of the COVID-19-severity course compared to NLR, irrespective of comorbidities (p < 0.001). Additionally, we determined that hypoalbuminemia in combination with AST (OR 1.003, p = 0.008) or TBIL (OR 1.657, p = 0.001) creates excellent prediction models for in-hospital mortality. In conclusion, the early evaluation of albumin levels and liver-related parameters may be indispensable tools for the early assessment of the clinical course of patients with COVID-19.