Sepsis: Given the patient's age, history of stroke, and presentation with progressive lethargy, weakness, shortness of breath, and confusion, sepsis is a highly plausible diagnosis. The high heart rate further supports this, as it is a common sign of septicemia.

Congestive Heart Failure (CHF) Exacerbation: The patient's shortness of breath and high heart rate could indicate an exacerbation of CHF, especially if the patient has a history of heart disease.
Pneumonia: This could be a cause of the patient's symptoms, particularly shortness of breath and confusion, and is a common issue in elderly patients, especially after a stroke.
Acute Coronary Syndrome: Although less likely given the description, an acute coronary syndrome (ACS) could present with shortness of breath and confusion in an elderly patient, especially if they have a history of heart disease.
Hypothyroidism Crisis (Myxedema Coma): Although the patient is noted to have hypothyroidism, a crisis could explain the lethargy, confusion, and shortness of breath, especially if the hypothyroidism is not well-managed.

Pulmonary Embolism (PE): This is a critical diagnosis not to miss, as it can present with sudden onset of shortness of breath and can be fatal if not treated promptly. The high heart rate is also consistent with PE.
Cardiac Tamponade: Although less common, cardiac tamponade can cause shortness of breath, confusion, and a high heart rate, and is a medical emergency.
Status Epilepticus: Non-convulsive status epilepticus could present with confusion and altered mental status, and is crucial to diagnose and treat promptly to prevent further brain damage.

Thyroid Storm: This is a rare but life-threatening condition that can occur in patients with hyperthyroidism but could be considered in the differential for any patient with thyroid disease presenting with severe symptoms, although the patient's hypothyroidism makes this less likely.
Neuroleptic Malignant Syndrome: A rare, life-threatening neurological disorder most often caused by an adverse reaction to neuroleptic or antipsychotic medication, which could explain the confusion and altered mental status.