When I started with my trainer 5+ years ago, one of my goals was being able to do a pullup. We never really focused on them specifically, I got up to 6, or so. The two things that really got me there, and they go together, were learning to activate my lats (pullups are as much a back exercise as an arm one), and deadlifts. They definitely don't work the lats directly, but you'll engage them when your form is good, training that activation under heavy load.

Problem is if you're thinking about a pullup bar, you probably don't have the equipment for deadlifts. Band deadlits can work, though.

You can also try a lat pushdown with a band to train lat activation. With pullups, it's easy to turn it into an arm exercise. It's harder to skip this with a lat pushdown.