FWIW
The only nuts used in the Levant engine, (just four from memory) in Cornwall are square nuts (probably made, with the bolts, by a local blacksmith; so unlikely to be a standard thread!)
The thick nut is there to provide the clamping load. The thinner lock nut is there to provide frictional load on the threads to prevent the clamping nut from loosening.
If the thin nut is fitted and tightened first, there has to be a risk of stripping the thread, because it will have less than 1D engagement.
My practice has always been to use locknuts on the outer side of the clamp nuts.
In contrast, the drawing instruction books, by A C Parkinson, used when we were at Technical College, showed the thin nut fitted first. The text advised tightening the locknut "with ordinary force", followed by "tightening the full nut upon it" and then slackening the locknut against the full nut.
This was bound to decrease the clamping force slightly, which in the longer term could result in movement, leakage from, or failure of, the joint. This advice predated the widespread of torque spanners.
Torque tightening produced, within the variations of the coefficient of friction between the male and female fasteners, a fairly consistent clamp load, and sufficient friction to prevent relative movement.
For a really secure fastening, use a mechanical locking method, castellated nut and split pin, tab washer, lockplate, or cross drilled nut/bolt head and wire locking. These methods were used, in preference to spring washers to ensure security of the hardware for Big End and Main Bearing caps in engines, or parts in transmissions.
The practice on Rolls Royce con rod bolts used to be to measure the length when slack and then to tighten the nut to produce a given extension. Since the characteristics of the bolt material were known, the clamp load would have been calculated, and so produced fairly consistently. This must have resulted in a secure fastening, since I can not recall any instance of a bolt coming loose.
For several years, now, Yield Tightening has been used to produce the required clamp load between parts, and to maximise the efficiency of the fasteners. This produces sufficient friction between the threads to prevent slackening.
For many years, now, Industry has used anaerobic sealants to ensure security of screwed joint systems.
Howard