@josh88 The problem with the question is the lack of standardization between lat pull down machines, specifically the number of pulleys, the type of cable (or rope), the friction at each pulley, the calibration of the weights and especially when you’re pulling circa body weight, how tightly you can jam yourself into the machine can make a difference.
They do seem to be rather similar for me in terms of reps at bodyweight if we’re talking strict form for both and I would be surprised if you could do a strict, full ROM lat pull down with your body weight for a few reps and not a by-any-means-necessary pull up.
I think some combination of lots of strict bent rows, strict lat pull downs (especially with controlled eccentrics), assisted pull up machines, and to a lesser extent, banded (minimally) and leg assisted (minimally) with tempo eccentrics.
To me the most important thing is that you are really stimulating back strength improvements in general which means that you’re putting in some solid work a few times a week. At least some of this work will probably be really challenging. But if you’re going through strict, full ROM back movements and progressing them then you’re headed in the right direction.
I think a mistake that many people make is overly focusing on the pull up itself when they have almost no ability (initially) to participate in the movement at all so I’m my opinion they need to spend some time getting stronger with some things that they can do, because failing a quarter ROM pull up once a week will never work on its own. Some people that are already able to at least do part of it or a reasonable eccentric might be able to make it work through stubborn effort and dumb luck, but I would contend that more back work would be good for them too.