I also need more informaton on your "friend." Male or female? How much do they weigh? Have they been training long? What is their approximate body fat percentage? Age? What are his/her goals relative to Pull-ups?
Forget the Lat pulldown machine or the gravity machines. To my knowledge there is no machine that can do what a simple bar can't do better! If you are trying to get better at horse back riding you learn to ride a horse! Same with Pull-ups. If you want to get better at Pull-ups or Chin-ups you have to actually work at that specific movement.
Depending upon how you answer the above questions, I would start with the person simply hanging from the bar. This does many things, not least of which improves gripping for that particular movement, and gets them used to hanging from a bar, which is essentially what occurs when you are performing Pull-ups.
If they are unable to hang for at least :30 we know we have a grip problem, relative to their weight. Perhaps their grip is not strong enough to support their weight. As I do not have that information as yet, I cannot make a judgement.If the trainee has no problem hanging from the bar then we can move on.
I would suggest that he/she perform half reps. As I have no idea of knowing where the trainee is the weakest in his pull I will suggest that they begin with pulling from mid range to the Pull-up bar. Get a chair and place it under the trainee, so that when he/she stands on it they are half the distance to the bar than normal. Then have them attempt one half Pull-up to the bar. If they need it you may spot them by pushing on their lower back slightly.
This will accomplish a couple of things. The first is that they will get a huge mental advantage in having touched their chin to the bar. The second, they will begin to build muscle and technique relative to that specific movement.
Finally, I would suggest that you begin by having them turn their hands around. Grip the bar underhanded, this is called a "Chin-up." I make this suggestion because more "Chin-ups" can be accomplished compared to "Pull-ups." This is because the bicep muscle is more activated with a Chin-up.
As of this date (1-2-03) I am able to perform 34 dead hang Chin-ups, while I can only do 30 dead hang Pull-ups. This means that I can do only 88% as many Pull-ups as I can Chin-ups. Actually, this is not bad, the ratio is not usually as good as this, perhaps between 65% and 75% as many Pull-ups as Chin-ups.
Post your friends statistics and I will try to be more specific relative to an actual training schedule.