Is a lactate level of 4.1 mmol/l (as distinct from 4.1 mg/dl) likely to cause pain?

Not likely: Lactic acidosis is not so much a cause of pain, but more a marker of poor perfusion, starvation, or other metabolic derangement. If we are still talking about the same patient as in the previous questions, low blood pressures and increased metabolic stress from critical illness can most definitely cause an increase in lactate levels.