A 28-year-old female marathon runner collapses at the 35 km mark during a competitive race. She is brought to the medical tent with severe fatigue, muscle cramps, and confusion. Blood glucose is 65 mg/dL, arterial pH is 7.28, and serum lactate is 8.5 mmol/L (normal <2 mmol/L). Her liver function tests are normal. Which organ is primarily responsible for converting the accumulated lactate back to glucose during the recovery phase?