Summary
This table summarizes the laboratory findings in patients with COVID-19 in China across the major recent studies. In brief, patients with COVID-19 have an elevation in liver enzymes (ALT/AST), an elevation in C-reactive protein, a decrease in procalcitonin. However, every other lab finding is generally non-specific.

https://www.nejm.org/doi/full/10.1056/NEJMoa2002032
https://www.thelancet.com/pdfs/journals/lancet/PIIS0140-6736(20)30211-7.pdf
https://www.thelancet.com/action/showPdf?pii=S1473-3099%2820%2930086-4
https://www.thelancet.com/action/showPdf?pii=S2213-2600%2820%2930079-5
https://www.bmj.com/content/368/bmj.m606
There are a few laboratory findings which predict worsening progression to severe COVID-19.
Abnormal Liver Function Tests

https://www.thelancet.com/journals/langas/article/PIIS2468-1253(20)30057-1/fulltext#tbl1
Patients with severe COVID-19 appear to have worse liver function tests upon hospital admission. Zhang et al. suggests this is from viral infection of liver cells due to virus binding to ACE2 receptors in cholangiocytes to dysregulate liver function.
Inflammatory Markers

Source: Ruan et al. Intensive Care Medicine 2020
https://link.springer.com/article/10.1007/s00134-020-05991-x
Ruan et al. showed that patients who died from COVID-19 have elevated Cardiac Troponin, Myoglobin, C-Reactive Protein, and Interleukin-6 levels than those who were discharged. From their experience, they confirmed that patients died from fulminant myocarditis and providers should be attuned to both lung and heart function during their hospital stay. They speculate there is a virus-activated cytokine storm that leads to acute cardiac injury.
Coagulation Markers

https://onlinelibrary.wiley.com/doi/full/10.1111/jth.14768
Tang et al. showed that patients who died from COVID-19 had significantly higher D-dimer, fibrin degradation product levels, longer prothrombin time, and longer partial thromboplastin times. In brief, the patients who died in their experience had early signs of disseminated intravascular coagulation and sepsis.