Let's use a less complicated example. If you have a wire (which can conduct etc. etc.) and move it inside / through a magnetic field, I'm sure you've seen the demonstration that there is a current that is produced. Brilliant, we can generate power, whipee! But ... you know ... what if I just kept going? I mean I could have unlimited power, right? Because there isn't any resistance ... so if I had a loop I could push the wire around and around and around and create a perpetual motion machine that makes me loads of electricity in complete violation of the 1st law of thermodynamics.
Yeah ... no. So Lenz law comes about because as the current (which will be opposite in direction to motion) will generate it's own magnetic field. This magnetic field clashes with the one it's already in, and you know that causes a force. This force is equal, and opposite, to the force you are applying to the wire to accelerate it. Now, if it was already moving that means you have kinetic energy; which we can understand? And then if suddenly generate a voltage (and all that jazz) then that's another form of energy so it has to come from your kinetic. That's the otherside of the coin. The force exerted onto the wire slows it down and converts that loss of energy intol usable (or otherwise) voltage.
So as the wire conducts, and uses that voltage, the kinetic energy of the shuttle must go down ... which means it's orbit goes down.