I'm trying to just do a home gym situation for now, because I don't want to spend the time to go to a gym. I'm doing pull ups, which has been great, and I'm also doing overhead presses and lateral raises which have been hitting my traps pretty good. But I'm looking to expand to more lifts that target the lat muscles than just pull ups. I don't have a lat pull, but I do have dumbbells. Is there anything I can do with dumbbells to target the lats and other back muscles?
The first question to ask yourself is what it is you are trying to achieve, or more specifically, why do you feel a need to do additional exercises to target your lats... what are you hoping to affect?
Size? Strength? Speed of movement? Range of Motion? Shape?
Without a Lat pull machine (and personally I prefer to avoid being restricted to using "machines"), pull-ups are the default that most people go to, because they are simple and effective. The trick is in HOW you perform the exercise. Where you position your hands on the bar (such as close or wide), whether your hands are held neutrally, or rotated palms towards or away from the body, all will change the difficulty and engage different aspects of the lat muscles.
Hands held close together with palms facing you will engage mostly the lats.
Hands spaced wide on the bar palms facing away will require you to engage mid and lower trap, as well as rhomboid muscles to assist in the pulls as you move your shoulders back towards the end of the pull up movement.
Developing assisting muscle can change how the lats present, as they can push the lats slightly laterally (outward).
Rows can affect the lats slightly, however rows with arms held horizontally or lower will engage considerably less lat, while rows angled above the horizontal begin to engage lats. This is because the lat pulls the upper arm (humerus) downwards (and also rotates it slightly). So rows effectively only exercise the lats in a very limited range of motion, and at the easiest part of the motion where the lats are their strongest and therefore don't necessarily need to engage fully. Rows are primarily for working Rhomboid and Mid Trap, however are great if your pull-ups are weak and you're trying to teach or rehabilitate your lats to pull better by gradually increasing the angle of the row above the shoulder.
With the home gym, you could consider using resistance bands at varying angles, or weighted pull-ups to build up both strength and size. Another option is to look into suspension training to change the loading on the muscles... by that I mean to teach them to pull under different conditions. Bands can simulate the cable pull machine to a certain degree, albeit with less "weight".
If you wish to stick with the dumbbells, you'd either need to use them as weights for pull-ups or hang yourself upside down to get your angles right to target the lats! And yes, I am joking... mostly!! Dumbells are primarily useful for pushing exercises. Pulls are limited to how you angle your body. Kneeling "rows" for example, which will target your Rhomboids and mid-upper traps more (depending on your body angle relative to the pull).
One of the other posters suggested rings as an option. Anything that is slightly unstable requires you to exert greater control of your movement, and that generally makes muscles work a little harder and requires more muscles to engage and stabilise motion. These are complex movements, as opposed to isolation movements which are done in a predominantly "stabilised" form and try to avoid involving additional muscle. Isolation is good at helping to sculpt/shape and build muscle, particularly when you're aiming for symmetry. If you're looking to build overall health and strength, and to be able to use your body in more day-to-day situations, complex exercises might be better.
I'm a big believer in training the body based on the situation you intend to put yourself in. My brother calls it getting "job fit", which I translate to mean "situationally fit". If you want to develop your lats for show, work them like a body builder. If you want to develop your lats for "working" or functional movement, work them that way. Climbing is a great way to develop lat and back muscles, particularly when you tackle climbs that require more arm and shoulder, as to avoid these muscles getting cooked, you need to engage the lats and back muscles more. In a home gym situation, a handful of holds to traverse can be easily created on a fence or a wall, or simply go to a climbing gym every now and then.
The lat pull down machine is a seated pull up machine.. if it's the same motion against the same line of gravity then it works the same muscles. Progressive overlead works with bodyweight too.
Doing 150+ non-stop easy repetitions builds as much or more muscles as 1 hard repetition but it's less dangerous for the joints. The hypertrophy range is just a stupid myth with no scientific foundation.
I suggest just buying rings and learning things like bulgarian pull ups or iron crosses and front lever rows.
But to answer your question, the best dumbbell exercises to target the lats are pullovers, rows and bent over flies.