There are a number of lens-related considerations.

1. The type of focusing motor used in the lens is a key factor. For example, Canon's USM or "ultrasonic" and Nikon's AF-S or "silent wave" motors are the fastest. Their respective STM and AF-P "stepper motor" lenses are fast, too... but not quite as fast as USM. The advantage of stepper motor is that they are quieter and smoother running, so might be better for video work. Another kind of focusing drive in common use is called "micro motor"... those are the slowest type... noisier, too.

Nikon also has used an autofocus system that doesn't use in-lens motors at all... some of their cameras have the drive motor in the body, instead. It's now only the D7000 series and higher that have that. Though fewer every year, there are still some lenses of this type in F-mount (the Micro-Nikkor 200mm f/4, as well as the Tokina 100mm f/2.8 Macro, for example). If used on the Nikon cameras without the in-body AF drive motor (current D3000 and D5000-series), those lenses will be manual focus only.

2. To a point, the lens' max aperture also plays a role in AF performance. Larger apertures let in more light, so there's simply more for the AF system to work with and AF will be able to work in lower lighting conditions. Plus,, while I don't know about other manufacturers, Canon cameras commonly have some AF points that are higher performance with lenses that have f/2.8 and larger max apertures. Usually at least the center AF point in a Canon DSLR is optimized for f/2.8 and faster lenses. (Note: In case you don't know, most modern AF lenses are kept "wide open" until the exact moment of exposure. They only stop down to a smaller aperture momentarily during the actual exposure.)

3. Some lenses are deliberately designed to focus slower. It is common for macro lenses and portrait lenses with exceptionally large apertures (such as f/1.2) to use "long throw" focus mechanisms. This is done because with at macro magnifications or fairly close distances with large lens apertures depth of field can be very, very shallow... demanding more accurate focus. In these cases the lenses are designed to emphasize focus precision over focus speed.

There also may be other design considerations. For example, a lens striving for particularly high focus performance might be designed

4. I have used a number of Canon IS (image stabilized) lenses over the last 20 years and always felt that it helped AF perform better. I have no way of testing and proving this, but it just seems to make sense that a lens would have an easier time focusing upon a stabilized image and subject. However, that doesn't seem to always be the case. Many Nikon shooters choose to turn off VR (vibration reduction) when they want the best AF performance possible, shooting highly active subjects. They feel that Nikkors with VR tend to focus slightly slower when it's enabled. I haven't used those lenses enough to say from experience and there does seem to be some evidence to support this... so I'll take their word for it. Note that there are bound to be some differences between stabilization systems. Canon IS, Nikon VR, Sigma OS, Tamron VC and Sony OSS all do essentially the same thing, but are each systems that have been patented by their manufacturers. I have heard that Sigma OS most closely mimics Canon IS (which was the first system to be implemented, in the mid 1990s). But, again, this is something I can't substantiate because I haven't used Sigma OS equipped lenses enough to say one way or another. I have even less experience with Tamron's VC and Sony's OSS (as in no experience at all).

5. Some lenses today have their own computer chips and firmware. In some cases, the user can access that and adjust how the lens works, including AF performance (speed vs precision). In other cases, the firmware can be updated by the user and that may improve AF performance. Newer lenses may use higher performance computer chips, too.

6. A lens also may have features like a Focus Limiter or a Focus Preset that the user can employ to help focus performance in certain situations. It's not uncommon for telephotos and macro lenses to have a Focus Limiter that can be set so that the AF system only works within a restricted range, speeding up performance. A couple of my Canon lenses also have buttons that I can program to instantly re-establish focus on a certain point. Say I'm shooting a horse and rider going through a course of jumps and decide to focus upon one of the jumps. I can pre-focus and save that info to the lens, then continue focusing and shooting elsewhere, then just press the button to re-focus on that one jump when they reach it. Of course, this can be useful with many sports and wildlife situations... really anywhere that subjects are moving relatively predictably.

7. A really simply thing that can help AF is your choice of lens aperture. When possible, stop down a bit. That will increase depth of field, which in turn covers for minor focus errors. Of course, you have to decide what's most important... if you are shooting in low light or trying to render a strong background blur you may need to use the lens' max aperture. But stopping down from f/2.8 to f/4 or from f/4 to f/5.6 when you can will help assure a higher percentage of in-focus, usable shots.

Familiarity with your gear and your lenses' AF performance comes with time. Yes, certainly it's noticeable. I see it in the results....

When I'm using a fast-focusing lens on a fast focusing camera and I set up both the lens and the camera correctly and am shooting familiar subjects, I get acceptable focus accuracy on upwards of 95% of my shots. When I'm doing something wrong, set something wrong or am shooting with less capable gear, or am trying to capture unfamiliar active subjects, I'll see my in-focus percentages drop.

I always say that autofocus today is far more accurate and much faster than I ever was able to focus manually... and I was actually darned good at it (and had faster reactions, much younger eyes).

I also think that three things affect autofocus performance: the lens, the camera, and the user. The most unpredictable of those factors is the user. Whether focus is right or wrong, it ultimately comes down to me. I know that many... probably most of my focus "misses" are my errors... not any fault of the camera or lens.