What will it take to fit 37's on a RCD 6in lift?

Will it work? Will it look odd?

It would probably look sweet. Id love to do it on mine. It would take an act of God. That, or some serious serious cutting. Youd have to cut the bumper, the valances or whatever the hay they call 'em, and youd most likely have to cut the fenders too. In the end it might be a little funny looking.

I'm sure I could run 37s if I had a 6 inch lift. It would look badass. You'll just need to do some fender cutting. Either do what's described in the link in my signature or get some bushwacker cutout flares.

35's fit easliy, I don't think you would have to do anything but mount them. I have 35's on 2 trucks with RCD and the next set of tires I buy will be 37's and expect no problems.

It's not the height of the tire it's the width you'd have to worry about.You might be ok with a BFG mud or all terrain.

What will it take to fit 37's on a RCD 6in lift?

Will it work? Will it look odd?
A body lift will make it work, but so will cut out flares with an aftermarket front bumper.

It's not the height of the tire it's the width you'd have to worry about.You might be ok with a BFG mud or all terrain.
painterjoe is exactly right- the tire width and rim offset is all it takes. If the RCD is a full 6" drop, 37's around 12.5-13.5" wide will easily clear.
Here are some pictures of 40's X13.5 wide on a Procomp 6" kit with wheels turned to full lock.