All frosty buddy
Yes, as two separate tracks, recorded simultaneously.
For my clean signal, I have a preamp/HPF pedal first in my effects chain that has a pristine DI out and that just goes straight into my interface. Everything after that in the pedalboard goes on the effected track.
Even if you don't have a dedicated DI box, getting something clean onto a track in your DAW is going to be useful, so deffo try the LS2 approach - it's all solid tinkering time and that's always a good thing, isn't it ?