Yes that's usually how it happens for me. This is a good sign as it means you are becoming used to being aware in dream enough that lucid dreams will just happen naturally, the same way regular dreams will.

This allows my dreams to last longer too, or at least chain them together. Because if one ends and another begins, I instantly (usually) catch that I am in another dream. So you can have a bunch of lucids in one night as you will realize what is happening each time you go into a new dream.