What are the most likely causes of a HAGMA in this case?
Both the high lactate and ketones >6 mmol/L will be contributing to the HAGMA.
This most probably reflects significant hypovolaemia, leading to impaired tissue perfusion and lactic acid production, due to diabetic ketoacidosis (DKA).
The glucose is <11 mmol/L and this therefore represents euglycaemic, rather than hyperglycaemic DKA.
Type B lactic acidosis due to metformin needs to be considered.
Given the clinical history and findings at echocardiography, cardiogenic shock leading to tissue hypoperfusion could also be a cause of lactic acid production. Myocardial function may be impaired by the severe metabolic derangement, however the severe biventricular impairment may be chronic or acute. There is no evidence given of acute myocardial ischaemia in keeping with an acute coronary syndrome.