Did this loop a couple of summers ago. We did it North lake - Lamarck - Darwin Canyon - Evolution - Muir Pass - Le Conte - Dusy Basin - Bishop Pass - South Lake. Won't give you a full trail report, instead I'm trying to remember the first portion as it covers the off trail portion of the trip.
Started the trip late in the day as I had come from the Bay Area and my friend from LA. We parked at the backpacker designated parking lot at North lake and then hiked a mile or so to the trail head. Continued up a couple of miles on trail to Lower Lamarck lake, it wasn't far but with the 1000 foot or so elevation gain it was slow going. Camped overlooking Lower Lamarck lake.
Next day we continued on trail for half a mile or so. Just before Upper Lamarck lake the trail disappears completely. We checked the map, and yes in fact the trail terminates right there for no apparent reason.
Looking around we found, then lost and then found the use trail that doesn't really go to Upper Lamarck, instead winds the most logical way towards Lamarck Col. Once we passed the confusion around Upper Lamarck lake it was really quite straightforward and the use trail clearly visible.
We knew that we were in the right place as we approached the little tarn below Lamarck Col. There was a permanent snow field there and a season of footprints that made the trail across it very clear.
Once at the top there was a very official sign welcoming us to Kings Canyon National Park. The next switch back or two going down was official looking trail, then nothing...Boulders, kerns, possible paths, but nothing that you can say definitely was the trail. So we just winged it and continue down. We could at this point see the lakes of Darwin Canyon so we knew where we were heading. We reached the middle lake, made camp, ate and went to sleep exhausted.
My concern for you is that you would be going in the opposite direction, heading from Darwin Canyon lakes up towards Lamarck Col. It is not obvious looking up from the lakes exactly where Lamarck Col is located, and there is no real use trail. The risk of getting completely lost is probably small as you have the Darwin Canyon lakes on one side and Mount Lamarck on the other, but you might spend many hours picking your way up through the boulders.