For what it’s worth, our principal cast on
Star Trek Phase II is outfitted mostly with custom made
TOS boots from Willies Shoe Service in Hollywood, California. Willies has made all the
Star Trek boots for Paramount starting with
Star Trek: The Motion Picture in 1979. They continue to make boots if Trekkies are willing to buy them. Expect to pay a nice sum: my boots made by Willie three or four years ago cost about $700. I don’t know what they are running now; I read that they are about $800 now. The good news is that that price is per pair, not per shoe.

They can and will make any style—the flatter heel style of the third season, the cool Cuban heel from the first season--whatever you want.
The earliest earliest Desilu
TOS boots were bought off the shelf. But early in the first season, they began to be produced by Western Costume. In what will likely be frustrating to you, a year or two ago,
Star Trek Phase II entered into a project with Western Costume to have a whole bunch of
TOS boots made using the original templates for “a song.” I think the price was a mere $300 if I recall. An order of a certain number had to be guaranteed by us before Western Costume would agree to the deal. In the end, we were just able to scare up enough people willing to pop for the boots. These weren’t custom made, exactly. They were made in a variety of fairly standard sizes. I haven’t heard of any plans to repeat this project.
Other options you have that are really close are Motorcowboy, Caboots, and Beatware. Lastly, sometimes people sell off their
TOS boots on ebay. You might get lucky there.
The only lace-ups I’ve seen are Shatner’s as he battles the Gorn and in “Tomorrow Is Yesterday” as he gets into a scuffle at the airbase. So they look to be pressed into service when he has to do stunts. I haven’t checked other
TOS fights to see if he wears them in other episodes.
Right. The lace-ups I recall seeing on Kirk during one of his knockdown fights. I suppose the lace-ups were used so as not to mess up the spiffier standard TOS boots.
I can't recall which eps screencaps I saw. One of Kirk's brawls, damned if I can't remember.