**Core Concept**
The patient presents with signs of acute limb ischemia and pulmonary embolism (PE), which are both manifestations of venous thromboembolism (VTE). VTE is a condition where a blood clot forms in the deep veins, breaking loose, and traveling to the lungs, causing a pulmonary embolism.

**Why the Correct Answer is Right**
The patient's symptoms of acute limb ischemia, such as swelling and decreased pulses in the left lower limb, are consistent with left common femoral vein (CFV) thrombosis. The positive D-dimer assay further supports the diagnosis of VTE. The CT pulmonary angiogram is a diagnostic tool used to visualize the pulmonary arteries and diagnose PE. The combination of these findings suggests that the patient has a pulmonary embolism, which is likely a complication of the left CFV thrombosis.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not a correct diagnosis in this scenario. While it's possible that the patient could have a pulmonary embolism due to a different cause, the provided information suggests that the left CFV thrombosis is the underlying condition.
**Option B:** This option is incorrect because it's not a direct consequence of the left CFV thrombosis. While the patient does have a positive D-dimer assay, which suggests VTE, this option does not accurately describe the diagnosis.
**Option C:** This option is incorrect because the patient's symptoms and diagnostic findings do not suggest a diagnosis of pulmonary embolism due to a different cause.

**Clinical Pearl / High-Yield Fact**
When suspecting pulmonary embolism, remember to also investigate for deep vein thrombosis (DVT) in the lower limbs, as they can be related conditions. A positive D-dimer assay can indicate the presence of a thrombotic event, but it's essential to consider other diagnostic findings and clinical context to make an accurate diagnosis.

**Correct Answer:** D. Pulmonary embolism due to left common femoral vein thrombosis.