I have a client who insist on using a lapis lazuli ( Royal Blue ) color because its part of their brand name. The rgb value is about R20, G30, B225. Can this be printed? Will digital printing be able to print better than offset printing as far as getting close to the RGB result viewed on screen?
An ink can not match that color. I doubt any ink system, such as CMYK, or even CcMmYyK, will match it. There's no way to get the same vibrance in standard inks. Digital printing, while it may accept RGB color input, still outputs CMYK or CcMmYyK It doesn't print RGB. RGB is a light spectrum you can't print light.
You might find a spot color (Pantone) that gets closer. You'll need to use a physical formula guide though. Do not trust software to match the color. I doubt you'll find an exact match, but you may get closer with a spot color than you will with an ink system.
In the end, it may come down to explaining to the client that not all colors are possible in print. It's a technological/physical limitation of ink on paper and it can not be circumvented at times. Impossible is impossible no matter how much it may be wanted.
Ink is going to alter the colors, as seen in the image when you convert it. The vibrance will be lost...
Scott has already covered the basics of RGB to CMYK conversions, so I won't go over the same ground.
If, however, you can persuade them to go with a spot colour, then purely on economic considerations, let them know about Reflex Blue.
It's not a match for their RGB values, nor as close as Scott's Pantone 2736, but the one advantage it has is it's ubiquitous. All offset litho printers will carry it in regular stock & the price will be factors below a ready-mix or even on-site hand-mix of a specific Pantone colour. The machine ops will be used to using it & know how it behaves on many types of stock. This makes the entire print run easier to manage & again keeps the cost down.
The other significant thing about reflex blue is it has a slight sheen to it, sort of "insect-like" - it also looks to have a slight red cast from certain angles in certain light. It's nowhere near as distinctive as those specialist metallic two-tone cars you occasionally see, but it does give it an "interest".
You could probably ask any print shop for examples to show the client.