Fun, fun.....try it on an CNC and you'll see how easy manual machines are at times.
On an internal thread (let's see if I can explain this clearly), I engage the half-nuts as though I were about to cut the thread, but no tool in the holder. I stop the spindle and making sure I have enough bar hanging out, slide it into the bore and push it into the existing thread. This gives me -Z- alignment. I do this with the crossfeed deliberately "large" so that the threading bar is sitting at an angle in the holder. Using my thumb, finger, or whichever digit fits, I hold the insert in place, aligned with the thread and crank the crossfeed in (smaller). When it gets in position, where it is properly to be clamped down, I lightly tighten one of the toolholder screws and then continue to crank smaller to get the insert tip out of the existing thread. Then I tighten the rest of the toolholder screws. As long as I didn't let anything shift in -Z-, I am pretty close to right on with the lead screw position. I can then back the bar out and if I was paying attention to the -X- position, I should know pretty close to where I am safe to take the first cut. Sometimes I blue the thread, sometimes not. Until you get comfortable with this method, back off sufficiently to clear the thread and while in thread mode, run the -X- axis (cross slide) out until you get contact with the thread. If all is well, you should touch it at the previously noted -X- position. Or close anyway. If not, you've missed something. If you are on, then carry on threading.
This can be a little awkward for shallow threads, as you don't have much time to determine whether you are accurately "timed" with the existing thread, so go slow. Turning by hand may be the solution in some cases. I have worked in repair shops where chasing threads was a nearly daily thing, so I realize it takes a bit of practice, and a 10 pound sack of nerves. But it happens every day in commercial shops, so we know it can be done. I will say it's much, much easier with external threads, and an approach similar to what I described for internal threads will work just as well. Just leave the threading tool loose and slide it into the existing thread before locking it down. All with the lathe set as though you were actually cutting, meaning nuts engaged, etc. Just coast the spindle to a stop somewhere in the threaded portion and do the tool position adjustment.
Clear as mud, eh?