You should not have any problems with the TRP Spyre. I put that on my Backroad in the rear. That is the first and only disc brake I have ever installed, everything went quite easily. I had a spare fork in the basement that was nearly the same specs (rake and the axle to crown length) as the Lynskey fork, except mine is for rim brakes. Thus my Backroad has disc rear and V brakes on front. I prefer drop bars, have that on all my bikes except for my errand bike.
The TRP instructions recommend compressionless brake cable. I used it. I do not know how important it is that you use it, but I had some so there was no reason for me to avoid using it.
I was pretty disappointed with Lynskey customer service, but by the time I finished building up my bike, I was quite happy with it.
I am running 45 mm fenders and 37 mm tires, my tires are Hutchinson Globetrotter, which I think is now discontinued, it is similar to a Schwalbe Marathon. I have several bikes so I only built up one set of wheels, if I want to ride on narrower tires I use a different bike. Including the Lynskey, I have two derailleur touring bikes and a Rohloff expedition bike, the Lynskey is my light weight touring bike. Plus some non-touring bikes too.
I have conventional hubs, not through axle. Some people complain that when they put a wheel into the frame with conventional hubs that their disc brake is never set right. But I have had no problem at all. If I pull my rear wheel out and put it back in, the disc brake is set perfectly.
I have one suggestion - there are replaceable dropouts in the back, each are held in place with a couple 4 mm bolts. Pull the bolts out one at a time and apply some blue loctite. (Blue is the version that can be removed with regular tools later, if necessary.) One of those bolts started to unthread on me on a short tour I was doing about a year ago. To make an extremely long story very short, I was fortunate I had all the tools that I usually tour with including a cassette removal tool. Thus, when that bolt started to make a total mess of things, I was able to fix everything. This past April I was on a group trip, one of the people had a new Lynskey that had the same dropouts. I warned her of that and she said that it had already happened to her too. So, it apparently is a common occurrence.
Just a quick heads up, if you have not bought a rear rack yet, you will find that the rear rack mounts up pretty high above the axle, much higher than on most other bikes. That means that your rear rack will be higher above the rear tire than typical.
Some photos of mine at this link:
Touring on titanium frame?
In the photos, the rear rack I have is a RackTime AddIt rack, you can see how high up it is. Fortunately I chose a rack that has the lower rails to hang the panniers from, if I had a rack without those lower rails my panniers would be rather high up.
Good luck with your build.