Word Choice – Difference Between ‘Their Own’ and ‘Themselves’

tl;dr The first sentence is much easier to understand, at least without context.

There are several different types of buses with their own dedicated lanes like a network in the city.

What "their own" does is emphasize that each bus has its own group of lanes, not shared with any of the other buses.

If "their own" were not there, it could become unclear if the lanes were dedicated to the buses as a group (the entire group of 5 buses gets 30 lanes), or to each individual bus (each bus gets 30 lanes, or 150 lanes in total).

There are several different types of buses with themselves dedicated lanes like a network in the city.

It's hard to imagine a case where "themselves" would work here, since "themselves" is a reflexive pronoun.

But here's a very contrived context where it could work:

Public transportation on the island is broken down into two types of transportation: buses and boats, each with their own dedicated set of lanes [the buses have a separate set of lanes from the boats].

There are several different types of buses with themselves dedicated lanes [each type of bus has its own set of lanes] like a network in the city.

What's happening here is that we're emphasizing layers of ideas. The buses are separate from the boats; and within the buses, bus A is separate from bus B.

I'd still much prefer the first one, though. I'd only use the second to avoid the repetition of "their own."

You mentioned in a comment an example in medicine:

Patients should be able to refer themselves to a specialist in such circumstances.

Here, "themselves" is being used as a reflexive pronoun together with a reflexive verb. The statement is that the patient is referring someone to a specialist, and that the "someone" is the patient.

It's not the same as in the bus example, where it only serves as emphasis. Here, it would be grammatically wrong to use "them"; instead, use "themselves," since the subject is the same as the object.

When in doubt, imagine replacing the subject and object with people:

Adam referred himself to a specialist.

Adam referred Adam to a specialist.

The first one sounds much less weird than the second, right?