The Friedewald equation for calculating LDL-C is invalid under which conditions?

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The key idea is that the Friedewald equation estimates LDL-C by subtracting HDL-C and a VLDL estimate from total cholesterol. VLDL-C is approximated as triglycerides divided by 5, which only holds reliably when the patient is fasting and triglycerides are not extremely high. If triglycerides rise above about 400 mg/dL, or if the sample is nonfasting (chylomicrons are present) or there are certain dyslipidemias that alter VLDL composition, the TG/5 estimate of VLDL-C becomes inaccurate. In those cases the LDL-C calculated by the Friedewald equation is unreliable, so direct measurement of LDL-C or an alternative formula should be used. The other scenarios listed don’t disrupt this relationship: extremely high HDL-C doesn’t affect the TG-based VLDL estimation, LDL-C being zero isn’t a failure mode of the calculation, and very low triglycerides (<50 mg/dL) still allow the approximation to hold.