Radio communications lost on climb out in IMC: when can I turn on course? Let's assume:


I have been cleared direct from Knoxville Downtown (KDKX) to London-Corbin (KLOZ) at 6000ft. The direct heading is 357°.
I lose comms after take off from runway 26, I squawk 7600 and I'm in IMC
Assume I cannot land where I took off


My plan is to climb to 6000 as filed but I can't turn northbound on course because of obstacles. When can I turn on course? Is the proper procedure to fly the back side of the localizer westbound till I reach 6000 and then turn?
Your assumptions are insufficient. 

If your clearance just states "CLIMB 6000 direct", and there are obstacles along the route, you have been given an incorrect clearance. 

It should have included the phrase "EXPECT" and an altitude and possibly also a time that would permit you to clear the obstacles.

Also, from your Skyvector link, it looks the Direct course parallels V97 very closely, which has an MEA of 5000, so you should not encounter any obstacles at 6,000.  Once you reach your clearance limit LOZ, you may initiate the approach.



Nevertheless If you lose comms you are expected to climb to the hugest altitude of 1. Your last clearance altitude 2. Minimum IFR altitude. 3. The altitude you were told to expect