Let's reduce it to a scale you might understand.
You are standing on flat ground, with a bucket of water in your right hand, it is heavy. You start to turn on the spot - you might even get up to 10 RPM. Are you a gyroscope? No? OK, continue.
As you pass a reference point straight ahead, you decide to raise the bucket shoulder high, with a stiff arm. Keep turning. The bucket comes up, but it isn't at its highest point when you are looking at your reference, it is some many degrees afterwards. This is a form of phase lag. The force exerted on the bucket took time to move the bucket upwards, and during that time, you kept turning. Are you a gyroscope? Hmm? Was it precession that made the bucket come up?