I would not perform dips, they are notoriously bad for your shoulders. If you want a long lifting career, do not do dips. There are other much better exercises to target the muscle groups dips focus on (lower pecs, lats, triceps) and in much better effeiciency and safety.
Your question is a bit difficult to answer because lats is a BIG muscle with multiple insertion and orgin points with fibers running in different orientations. As with the pecs, any fan shaped muscles will require diferent exerciese to targte different portion of the muscle group.
If you cannot perform pull ups at this time, you can perform pull downs with a bar with a lat pull down machine. This way you have a choice of not immediately going for your full body weight as a source of resistance.
The key to remember with pull down machines are these:
1. Do not jerk the bar down with your trunk. You are not doing trunk extension here...
2. Do not pull down the bar behind your neck. this actually will target alot of the upper trapezius (as according to EMG studies) and the posiition is terrible for your shoudlers.
3. The narrower the grip of your hands, the more you will use your biceps. To grab the bar with hands much wider than your scapular angle (V shaped from your shoulder blades) makes the movement very akward. This is because the insertion of lats is on the front side of your shoulders (yes lats is a shoulder internal rotator) and grabbing the bar too, too wide does not give you full range shoulder adductions with internal rotation.
4. Grabe the bar with your palms facing away you. If you grab the bar with the palms facing you, youa re doing forearm supination. one of the 3 major functions of biceps is forearm supination. If you grabe the bars this way, you will recruit more of the biceps again...
5. Make sure youa re not performing the lat pull downs with just bending your elbows (elbow flexion). This is not fully utilizing the lats inthe areas of shoulder depression. You want to perform both shoudler depression AND shoulder adductions. Meaning you do not only have to pull the bar down with bending your elbows, but your shouders should not be as high as your ears... Shoulders both have to come down as the elows bend...
Again, there are many other lats exercises to be performed. Pull ups and pull downs tend to recruit the lateral (side) portions of the lats, which achieves the wide look. To recruit the middle/lower, and lumber (back) lower portions to achive that thickness look, you need to perofrm other exerciese such as different kinds of rows..
Best luck with your training, and train safe!