Periprosthetic Neuroma or Neuropathic Pain: This condition is a common cause of persistent pain after total knee replacement (TKR), especially if the pain is localized and burning in nature. The intense burning sensation on the lateral aspect of the tibia could be due to irritation or damage to the peroneal nerve or its branches during the surgery.

Complex Regional Pain Syndrome (CRPS): Although less common, CRPS can occur after TKR and presents with intense burning pain, swelling, and changes in skin temperature and color. The lateral aspect of the tibia could be involved if the condition affects the lower limb.
Heterotopic Ossification: This condition involves the formation of bone in soft tissues and can cause pain and inflammation around the knee after TKR. While it might not typically cause a burning sensation, it could contribute to discomfort and pain in the area.
Loosening or Malposition of the Prosthetic Component: Mechanical issues with the prosthetic components can lead to abnormal stresses on the surrounding bone and soft tissues, potentially causing pain. However, the pain is usually more diffuse or related to specific activities.

Deep Vein Thrombosis (DVT) or Pulmonary Embolism (PE): Although DVT and PE are more commonly associated with swelling and acute pain, it's crucial not to miss these potentially life-threatening conditions. The burning sensation could be an atypical presentation, especially if there's associated swelling or redness.
Infection: Prosthetic joint infection is a serious complication that can present with pain, swelling, and systemic symptoms like fever. The burning sensation could be part of the symptom complex, especially if the infection involves the soft tissues around the knee.
Osteolysis or Periprosthetic Fracture: These conditions involve the destruction of bone around the implant or a fracture near the prosthetic component, respectively. Both can cause significant pain and require urgent attention to prevent further complications.

Chronic Regional Pain Syndrome Type II (Causalgia): This is a rare condition characterized by burning pain, usually after a traumatic nerve injury. It could potentially occur after TKR if there was significant nerve damage during the procedure.
Nerve Entrapment Syndromes: Conditions like common peroneal nerve entrapment or tibial nerve entrapment could cause burning pain in specific distributions. These are less common after TKR but should be considered in the differential diagnosis.
Referred Pain from Other Sources: Rarely, pain from other sources (e.g., lumbar radiculopathy, hip pathology) could be referred to the lateral aspect of the tibia, causing a burning sensation. A thorough evaluation of the patient's symptoms and additional diagnostic tests might be necessary to identify such causes.