the knife hasn't shipped yet, so (i think) the only person who could measure anything would be Tomso @ Lion Steel.
RYP is en route to Somalia (last i heard) so i don't think he'll be able to measure anything until he returns.
not sure what pics you're looking at, but some of them are digital renderings, not actual photos... and the blade is 3/16" or so thick, so that may make other parts of the knife look thinner.
by "relief cut" i'm assuming you're referring to the thin section at the base, or butt end of the lockbar?
here's an edge-on pic of one of the prototype knives, and if the blade is .1875" i'd expect that p part you're asking about to be .0625".
but i think the knife is built in metric. so the blade is "between 4 and 5mm" (quoting Tomso from memory, not sure exactly where i read that tho), and the thin part on the lock is perhaps 1.5 or 2mm.
all i can do at this point is look at the pix and guess.