Originally, lavalier mics were buried in the chest area and painted to match the costumes, where possible. Now, lavaliers are mostly mounted on the head, above the hairline underneath the wigs, if the actors are wearing wigs — or on mounts over the ear if they're balding or have thin hair.
The best audio placement for a lavalier is probably the last place the director wants it: Dead-center and as far down the forehead as possible is the preferred spot. The center of the forehead just sounds fabulous — it's really a good place to put a mic. It's very visible, but as you move farther away from the center of the forehead, you have to make more EQ adjustments to make up for it.
Avoiding perspiration is important. A drop of sweat has the same effect as putting your thumb over the microphone. It's just like switching it off.
Hats are another problem, because they create a reflection from the brim. You see a strong reflection in a small set of frequencies, almost like a shelf. If need be, you can mount the mic on the hat and switch back to the head mic when the hat is taken off.
So with 24 mics in a show, you might need 30 or more microphones mounted on various hats and actors' heads and things like that. It's not uncommon now to have at least one, if not two or more, people backstage chasing microphones, checking that they're really in the right place, that they're working before they go onstage.