LUTs are only part of the profile process. Color Profiles are not LUTs but simple rely on LUTs to function. To explain the whole process can get a bit complicated. Suffice to say that there are both graphics and video versions of color profiles. Graphics color profiles have the goal of synchronizing what you see on the display with what you see on printed output. Color profiles exist for everything in the chain, monitor (display), graphics card, OS, software and printer driver. And don't forget the color profiles in the camera. Some of the profiles are fixed, others can be tuned. Fine tuning can be achieved using a color profile sensor device as mentioned previously. If one is serious about the accuracy of the print, a larger investment can be made to create custom printer profiles using a spectrophotometer to test the colors of the printed output. It's a different device than the one you use on the monitor because monitors are backlit illuminated transmissive panels where paper is a reflective color source.
With printed output, many things influence the color, most of them are after the computer. Printer hardware, ink formulation and type, paper color and type and the color of the light in the viewing area.
Those who work in the commercial graphic arts, esp those who are involved in printing can probably comment on this far better than I can. I haven't done it for a long time and the technology is much better now. But color matching has been a major challenge and goal for decades even before computers.
Here are some links for general info/explanations of the computer part of it...http://www.optirep.net/lut-profile/http://www.dpbestflow.org/color/color-management-overview#cmykhttp://www.colorwiki.com/wiki/How_To_Get_My_Monitor_To_Match_My_Printer
If you go down the road of color matching, you are in for a wild ride. Personally, unless the printing is going to make or break you, I would settle for simply calibrating your monitors and leave it at that.
Also, how do you have you monitors situated in the room
? It's important that any light sources like windows are in front, not behind you. Light reflections create irritating glare and reflections on the screen not to mention washing out colors. (This is why I hate glossy screens. Most true serious graphics monitors are matte, not glossy, to reduce glare and reflections.) Make sure your editing area is not too bright and you aren't fighting light bouncing off your monitor in your eyes. Also, keep the monitor at the correct height to prevent neck and back strain.