You can contact a local tourist agency to make your bookings..
or you can contact the hotel agencies at a lower altitude to make bookings...this can be done too..
Sadiya dont worry about anything the place is very cooperative.. for north sikkim like lachen and lahchung you need a pass which you can get easily from mangan for free you need to put your aadhar and photo with you. mangan is nearly 4-5 hours far from gangtok and you can easily get every hotels and accomodations at cheap rates . hotels are few there at lahchung side but at lahchen side dont stay at lachen there is a place near to lachen 'thangu valley' that will your awesome experience and guru dongmar lake is near from thangu valley as tge timings for this are very short so i recommend to stay at thangu valley where you get home stay. but another thing after some time the climate become very harsh that side so think fast avout that