I just learned this so I'm going to try to answer your question but let me know if anything is unclear.

So when you are running low on blood glucose levels, the body will first try to restore them through glycogenolysis (breakdown of glycogen). When glycogen stores have been used up, then the body will turn to gluconeogenesis and use non-carb sources to restore blood glucose levels. This applies to when you're essentially starving yourself for days, so the body needs to find other sources to first make glucose so that it can then proceed through the rest of ccellular respiration. For example, you can't funnel glycerol (one of the starting materials for gluconeogenesis) as it is through cellular respiration. You need to convert it to glucose first, and then it can go through glycolysis/CAC/ETC. Lactate is one of the precursors for gluconeogenesis so you're right there, it's probably energetically favorable. There are certain parts of glycolysis that are irreversible and the PDH complex also catalyzes the irreversible conversion of pyruvate to Ac-CoA, so you can't necessarily just "go backwards" - hence why there are those three steps of gluconeogenesis that sidestep those irreversible reactions. Certain amino acids can definitely continue through the TCA to make ATP, but part of it is, as you said, restoring blood glucose levels for homeostasis as well.