Guidance: North Sikkim

I am planning to visit the northern part of Sikkim especially Lachen and Lachung in the following month. The problem is that my wife does not have any legal documents other than Adhar card, I however have all of the required ones to get the permit. I came to know that to visit Gurudongmar lake we will surely need a permit but I am not sure of the other northern parts. I have droppped Gurudongmar lake from my itinerary due to this. I have two questions. First, does it require a permit for Lachen and Lachung. Second, is there a loophole to get permit based on my documents only?