LC eating rapidly induces insulin resistance. This is a completely and utterly normal physiological response to carbohydrate restriction. Carbohydrate restriction drops insulin levels. Low insulin levels activate hormone sensitive lipase. Fatty tissue breaks down and releases non esterified fatty acids. These are mostly taken up by muscle cells as fuel and automatically induce insulin resistance in those muscles.
This is patently logical as muscle runs well on lipids and so glucose can be left for tissues such as brain, which really need it.
However, while muscles are in "refusal mode" for glucose the least input, from food or gluconeogenesis, will rapidly spike blood glucose out of all proportion. This is fine if you stick to LC in your eating. It also means that if you take an oral glucose tolerance test you will fail and be labelled diabetic
The general opinion in LC circles is that you need 150g of carbohydrate per day for three days before an oral glucose tolerance test.