Leo

Nope. You got it right, but you just don't do that. Instead use an effect pedal to change the lead sound if you like. You don't use the amp's distortion channel.

I put mine at the end of the effect chain - play a clean or dirty part - sample it - play a clean or dirty part over it.

Or...

You could use two amps and a loop selector A/B switch to have the Loop Station play using ONLY that specific amplifier and then switch to the other amp for other parts.
That is a bit too complicated for my tastes.