Using LUTs in CMYK files

when I add the LUT but then convert to CMYK after it doesn't seem to save the LUT effect.

Please provide meaningful information, how exactly do you convert? (Post screenshots please.)

Yep, apply the LUT to the RGB,

if you get the right look - then send that RGB to the printer,

if they want only CMYK then you need to know specifically which CMYK ICC profile to use,

then flatten the RGB and convert.

I'd get a certified proof to be sure. 

Is your own computer display calibrated and profiled?

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

First, it is very likely that the print vendor will be okay with an RGB image. Most large format, inkjet type printing produces better results with RGB images.

If you must provide a CMYK image, do this.

1. Apply the LUT to an RGB image
2. flatten the file
3. convert it to CMYK.

@Attract & Engage 

If the LUT is RGB based then it must be applied in RGB and then converted to CMYK if that is the requirement (view at 100%).

What LUT? Sample images and or custom LUT files would be helpful to fully understand your issues.

P.S. There should be no technical reason why they can't use RGB files with modern software, but that is a side issue. This is a workflow choice and requirement dictated by the PSP.