First of all, I have no idea to which cdo (depot)/dvsn/zone this rake was allotted to. So i couldn't answer ur query.
Per say, even if this rake is allotted to kakinada cdo (which of crs have the least chance), then too, I am guessing gowtami would be the prime contender for lhb rake as it has end to end e loco connectivity, which doesnt require LR, such that HOG loco can be provided to it. Also, it's LPI partner, Narayanadri runs with HOG loco at times, and LSA can be established between these.