Hmm...I thought I'd do a quick lookup in my old biochem text and give you an answer, but I'm not sure. Yes, there is a respiratory pathway that works via gluconeogenesis starting from lactate, but there's a paragraph commenting on lactate and "new research" which would now be almost 20 years old (it's an old text) that sounds like there could be some other direct pathway, but I have never had an interest in continuing to follow that literature to help with whether something would have been updated on that or not. So, unfortunately, I'm unable to answer this question and will have to defer to someone with more current knowledge in that topic.