1D Mark III? 1Ds Mark III?
What you see on the LCD of any DSLR is a small "preview" JPEG. It's of limited value, but you probably can modify the appearance to be a bit more acceptable. (I don't have either of those cameras, so what's below is based upon every other Canon I've used).
Look for the Picture Styles in the menu: Standard, Portrait, Landscape, Neutral, Faithful, Monochrome, User Defined 1 through 3.
These are typically used as simple preset choices when shooting JPEGs with the camera. The three user defined ones can be custom setups. But the Picture Style that's chosen also determines what appears on the LCD, even when you're shooting RAW files. Choose a different one that gives you more pleasing colors, you'll need to experiment. I think Canon may have some info on their website how the different Picture Styles are set up. You can also go into the setup to check how the different parameters are adjusted, make any changes and increase sharpness, if you wish.
These settings will effect any JPEGs you shoot. But they will not effect RAW files, unless you post process them with Canon DPP and allow it to default to the Picture Style. Even then, with RAW files you can change it if you wish, the original file data is not modified.
Still, the LCD on any DSLR is only marginally useful for image review. It's too subject to ambient light and there is no way to color calibrate it accurately. You can zoom in to check focus and check overall composition. The histogram can be very helpful with exposure accuracy. But critical image color and contrast evaluation, along with focus accuracy, are best checked on a calibrated, graphic quaility computer monitor. How about shooting tethered?