First of all, sRGB is a single color space, with defined boundaries and defined mappings from RGB values to (for example) CIE XYZ values, a specified viewing environment, etc.

CYMK, by contrast, is really a whole family of color spaces. All the color spaces in the family are subtractive, but you can't count on them having a lot in common beyond that. The exact colors of the primaries (i.e., the shade of cyan, magenta, yellow, and even black) vary. Since CMYK is used almost exclusively in printing, the color of the paper, brighteners, ability to accept ink, etc., all affect perceived color as well.

From a theoretical viewpoint, there's no question that conversion from RGB to CMYK can be completely lossless, so (for example) you can do a round-trip conversion (RGB to CMYk, then back to RGB) and guarantee that the result is identical to the original input.

From a practical viewpoint, CMYK (as noted above) is used almost exclusively for printing. That being the case, the real question is whether there's a real printer that can display the entire sRGB gamut. Although I could be mistaken on this, I believe the answer to that is no. In addition to that, it's difficult (probably impossible, really) to get exactly the same look on paper that you do on a monitor.

In particular, paper only reflects light that's shining on it, and the ink on the paper restricts the amount that's reflected. That means under normal lighting, what you see on the paper is always at least somewhat less bright than the ambient light.

A normal monitor emits light. Especially the higher-end monitors typically used for photo-editing are typically used in a relatively dark environment, and often have hoods as well. As a result, the monitor is typically brighter than ambient.

A gallery will typically attempt to display prints a bit more as you see them on a monitor, with lighting directed on the picture that's substantially brighter than ambient. Proofing boxes generally do roughly the same.

Bottom line: even though sRGB to CMYK can be lossless, it normally isn't -- and since it's normally for printing, really shouldn't be, except in the rare (nonexistent?) case of a printer that covers the entire sRGB gamut.