Yes, the liver has MANY functions. One is to store 'emergency' glucose in the form of glycogen.
When the blood glucose levels drop a bit too low, the liver 'dumps' some of its stored glycogen/glucose into the bloodstream to bring the glucose level back up to the 'comfort level'.
When our bodies have been living with raised blood glucose levels for a while (as your body has), then it learns to adjust and cope, and starts to think that high levels are normal. So it may trigger a liver dump if your blood glucose levels dip below the current comfort zone.
Fortunately, just as it learned to adjust to unhealthy high levels, it can learn to re-adjust to the healthier lower ones. So as you get used to the new way of eating, and your blood glucose levels drop back to normal, you will get fewer liver dumps as everything comes back into the healthier range.
(the liver dump is actually a very useful and very necessary survival trait. it means that we can get sudden bursts of glucose dropped into the blood stream in emergencies - like running for a bus, or dealing with an emergency. it is just that when blood glucose levels get too high through uncontrolled diabetes, things get out of wack for a while.)
Hope that helps.
Oh, and the pancreas is the organ that (amongst a lot of other things) produces insulin. Insulin is the hormone that takes blood glucose out of the blood and stores it in cells for immediate use, or for fat storage. So the pancreas' insulin, and the liver's glucose dumps need to be harmoniously balancing each other, in order to maintain healthy blood glucose levels.