Interested and been looking at this for a while.

One of the things I stumbled across is the connection between blood glucose levels and the thyroid hormone T3, it seems that if blood glucose level falls, then in order to conserve the glucose, the body produces reverse T3 which results in a lowering in T3 levels, which induces a lowering of basal metabolic rate and hence a reduction in glucose consumption, I have seen this refered to as the "Hibernation Response".

Following the line of thinking, a low blood glucose level on a very low carb diet would most likely be due to inadequate gluconeogenesis, and although it is not necesarily the only cause it appears that high leptin levels (leptin resistance) can impact negatively on this.

As leptin resistance often precedes insulin resistance by decades, does this mean that these individuals are pre-pre-pre-diabetic and that leptin levels should be checked before diving into a low carb diet.

Leptin seems to have many fingers in the pie of glucose homeostasis and depending on areas affected including accessing hepatic glycogen, so some individuals can not do any low carb meals at all while others can low carb for a day, but if they go for a week their FT3 levels fall and their metabolism slows down.

The other interesting thing was the link between low T3 and High LDL

Here's some of the links I looked at in order of relevance, sort of:
High LDL on Paleo Revisited: Low Carb & the Thyroid | Perfect Health Diet
Low Carb High Fat Diets and the Thyroid | Perfect Health Diet
The Daily Lipid: The Central Role of Thyroid Hormone in Governing LDL Receptor Activity and the Risk of Heart Disease
What is leptin's relationship with PEPCK? -
The role of leptin in glucose homeostasis - Denroche - 2012 - Journal of Diabetes Investigation - Wiley Online Library
Comparative acute effects of lept... [Cell Biochem Funct. 2005 Nov-Dec] - PubMed - NCBI
Leptin resistance and the response to positive energy balance
Fasting plasma leptin level is a sur... [J Clin Endocrinol Metab. 2010] - PubMed - NCBI
Central role of cAMP in the inhibiti... [Pol J Pharmacol. 2004 Mar-Apr] - PubMed - NCBI
Melanocortin-independent Effects of Leptin on Hepatic Glucose Fluxes