When can motorcyclist ride three abreast in the same traffic lane?

Never unless they are in a parade. The safest way and the way that they are supposed to ride is in a staggered fashion. The first bike should be in the left wheel lane and the next bike should be behind that one but in the right wheel lane. This enables the bikes to manuver safer in case one has to swerve away from an object and it keeps the second bikes view clear of what is ahead. This also makes it easier for cars to see the motorcycles. This staggered pattern should be continued with all bikes that are in the same group. What you see in the movies and on the old tv show "Chips" was a very dangerous way to ride and set a very bad example. Those bikes were on a trailer being towed behind a camera vehicle.