What happen to the fat we eat with lchf diet.

Although there is no completely simple answer, the VERY basic answer would be if you eat more calories than you need it can still get stored as fat.

To get into the body fats (triglycerides) are broken down into monoglycerides and free fatty acids, then imported across the intestinal wall. Once inside the cells of the intestinal wall they are recombined back into triglycerides and then packaged along with cholesterol into a phospholipid vesicle that are water soluble, otherwise the fat couldn't get transported in the watery circulatory and lymphatic systems.

These phospholipids then get transported to both the liver and fat cells. Where it is either stored or processed.

The various metabolic process that are going on continuously in the body are quite complex and interwoven. There is no one single process running at one given time, rather  all of the various pathways can be occurring simultaneously in different cells in different areas of the body.

There could be some fat cells storing more fat in one area while other fat cells are either processing the stored fats for energy or releasing them as phospholipids back into the bloodstream to be processed  in the liver.

Some cells could be processing glucose, others processing free fatty acids through the krebs cycle and still others processing ketones. 

The human body is a wonderfully complex system that is far from being fully understood.

Because the low carb keeps the body in a fat burning mode more consistently.

When the blood sugar level rises the pancreas will start to produce insulin so that the cells can absorb the glucose and utilize it, but it has the secondary effect of turning off the metabolizing of fat.

If you stay in a state of ketosis by limiting carb intake and there by limiting insulin production the body will metabolize more fat.

Agreed.  High sugar (carbs) =  high insulin = fat storage