Your logic is correct. During insulin tolerance, the liver ramps up production of new glucose molecules because it thinks the body is starving (via gluconeogenesis). To perform gluconeogenesis, the liver uses fatty acids, lactate, and glucogenic amino acids and converts them over to glucose.
Normally, insulin inhibits an enzyme called PEP carboxykinase in the liver. This signal prevents the gluconeogenesis pathway from starting. However, in insulin resistance, target cells don't respond to pancreatic insulin and this enzyme isn't inhibited as well. Therefore PEP carboxykinase starts working and converts precursors into glucose. So, your correct so far. But because there are so many different compounds that can produce new glucose molecules, blood lactate levels don't drop too quickly or dramatically. Another point to consider is that diabetes can naturally increase lactate levels. It can increase it to such a degree that some diabetic patients can get lactic acidosis. This is because during fasting periods of diabetes, there's an increase in whole body non-oxidative glycolysis (Yong Wu, 2016) which would increase lactate synthesis.
Summary: There is dramatically increased lactic acid synthesis by the body. Marginal reduction in lactic acid by the liver via gluconeogenesis. This ultimately leads to elevated lactose levels.
When your professor says, "diabetic rats don't perform gluconeogenesis." I think he's trying to simplify the answer. What is actually going on in your experiment is that something in your methods is probably inhibiting gluconeogenesis by some means. Maybe you're using a weird genetic mice knockout that also knocks out the gluconeogenesis enzymes. Or maybe your using a specific chemical like 6-mercaptopicolinic acid which is a potent gluconeogenesis inhibitor. Ultimately, knocking out the gluconeogenesis pathway would increase lactate levels even higher than normal. But normal can be elevated as well.