This is an uncommon side-effect of having a massive amount of propofol over a short period of time.
The timeframe seems to be around 48 hours, and one requires quite a good amount of propofol for this to happen – about 4mg/kg/hr, or 28ml per hr of straight propofol for a 70kg adult male. Seems like a lot – but considering that this male might be struggling vigorously against the ventilator, irritating the nurses, propofol rate keeps going up, boluses happen for pressure area care et cetera… One can see how such a thing could happen.
An excellent article is available as a pdf, from 2007 by Professor Kam (yes, THE Kam from RPAH).
The mechanisms of lactic acidosis in propofol infusion syndrome (PRIS) is likely the inhibition of cytochrome C and coenzyme Q; like cyanide, this results in a failure of the electron transport chain. Furthermore, fatty acid oxidation is disrupted, which results in reduced acetyl-CoA availability to Krebs Cycle; the excess of fatty acids builds up and inhibits electron transport even more (aside from contributing to the acidosis).
Underwood, Ao H., and E. A. Newsholme. "Properties of phosphofructokinase from rat liver and their relation to the control of glycolysis and gluconeogenesis." Biochemical Journal 95.3 (1965): 868.
Kam, P. C. A., and D. Cardone. "Propofol infusion syndrome." Anaesthesia62.7 (2007): 690-701.
Marinella, Mark A. "Lactic acidosis associated with propofol." CHEST Journal109.1 (1996): 292-292.
Vasile, Beatrice, et al. "The pathophysiology of propofol infusion syndrome: a simple name for a complex syndrome." Intensive care medicine 29.9 (2003): 1417-1425.
Schenkman KA, Yan S. Propofol impairment of mitochondrial respiration in isolated perfused guinea pig hearts determined by reflectance spectroscopy. Critical Care Medicine 2000; 28: 172–7.