Like I said, I am not a fan of the C1 catalog. Because of that, I have a LR as well as C1 catalog. When I need to find something quickly, I use the LR catalog. When I need to edit something quickly, I use C1
I do not use any folder structure though. I find LR's cataloging/key-wording sufficient for finding photos and Collections sufficient for keeping certain shoots together.
You can make C1 and LR play together nicely and keep your LR catalog function as is.
A workaround is this:
Open C1 and create a session called "default Session" or whatever you like.
Within the session library tab, navigate to system folders. Within here, you can then find your desktop or wherever you would like to keep the raw files temporarily. Create a folder and name it "C1 Conversion"
Keep the LR catalog as is. Export copies the raw files you want to massage in C1, to your "C1 Conversion" folder.
All this could be accomplished by creating a Preset in LR. In the Post Processing section of the preset choose "Open in other application". Then designate C1 as that application.
Use sessions to work on your files. Export said files as jpeg or tiffs and import those back into LR. Then delete raw copies mentioned above.
One thing I like to do is add "C1" to the naming of the converted file. That way you know it was converted using C1. Its helpful in determining which raw conversion you prefer later on.
You still keep your LR catalog in tact while being able to use C1's conversion.
This is how I did it for a long time and was OK with it.
I'm finding that having both softwares is a good thing. There are some files that are better suited for one or the other.
C1 does not do well with noisy images in my experience. LR tends to do better. Also My D800E files are a little to orange for my liking and is a pain to get right. (This may have changed with the new color controls)