I recently purchased a Nikon L35AF 35mm point and shoot. The seller clarified it didn't come with a lens cap. Are there lens cap that would fit this camera if it's the right size? Or is the one that comes with the camera the only one that fits?
In general there are different sizes, and mounting types. Slip on, or squeeze style being the most prominent types and sizes can range quite a bit. So they arent universal by any stretch.
That said, the L35AF lens cap had a custom cap that also protected the viewfinder. There are people apparently who use just a standard 46mm lens cap however. So while not universal they aren't generally proprietary down to a per lens basis.
For interchangeable lenses that take a screw-on filter and where the cap fits into the filter thread with spring/tension, most front lens caps are going to be made in a standard filter size, and they're relatively easy to replace (Leica Series filter sizes being one notable exception and a serious PITA to find caps/filters for).
Back lens caps, otoh, are going to be specific in thread and size to the mount system of the lens.
However, for a fixed-lens camera, like the Nikon P&S you're talking about, where the lens cap slides onto the end of the lens, chances are good it'll be hard to find a replacement that's an exact fit, and you may have to find the original part. There are no standard sizes for those types of lenses.
No. Lens caps are not universal, although many are interchangeable. For most lenses with a thread and no built-in hood, all you need to know is the thread-size and you can buy a cap of the same type and diameter.
There are many proprietary hoods which are designed to mount over a built-in hood or dome over protruding lens elements. Those are almost never interchangeable.
For fixed-lens cameras, most have self-closing lenses. Those that do not, nearly always use custom lens caps. Although for popular models, third-party sometimes offer compatible caps. Your best bet is to search for lens can for L35AF and see who has something to offer. Some may sell used originals, some may sell third-party made ones.