We make glucose via gluconeogenesis. So, too, we make glycerol via glyceroneogenesis. And we recycle ~50-65% of the FA's released via lipolysis back to trigs.
One interesting thing is the behavior of brown adipose tissue. The enzyme responsible for re-esterification, PEPCK-C is high in BAT. But interestingly enough insulin INHIBITS this enzyme while a high protein zero carb diet stimulates it.
There's lots more here to digest. I'll revisit this post and update.