Viruses can fully reprogram the cells and produce a ton of viral proteins before the cell is exhausted and dies. Some of the proteins will assemble into viruses, some of them will be released as an overflow into the circulation. Some of these proteins may permeabilize RBCs while others may bind to hemoglobin. The latter ones may only be a catalyst, releasing heme from the hemoglobin over and over thus multiplying the effect by a great deal. Also, free hemoglobin is highly toxic, so even a small percentage can cause a lot of problem in the lungs.