Yes, occult malignancy, malnutrition and chronic liver diseases can lead to low LDL-C levels. In addition, abetalipoproteinemia and familial hypobetalipoproteinemia, which are relatively rare inherited diseases, can also lower the LDL cholesterol levels.

If associated with elevated HDL-C it might be due to CETP deficiency (rare). In patients with septicaemia/sepsis, first you observe a decrease in HDL-C, followed by a decrease in LDL-C. Patients with mild-to-moderate infection do not show decreased LDL-C levels. A last possibility that comes into my mind is hyperthyroidism which associates primarliy with decreasesin LDL-C, HDL-C levels may vary in these patients.