There are at least three different gamuts:
1) The gamut of the RGB you are working in. LR uses a version of Prophoto RGB and that should eliminate that problem.
2) The gamut of your monitor. Some colors cannot be displayed on your screen.
3) The gamut of your printing device
2-3 are covered pretty well by Lightroom's "softproof". I would recommend the Lightroom videos here on LuLa where Jeff Schewe explains hot it works. I'm sure there are other good descriptions.
Bill referred to a video with Julianne Kost. I have not seen that video but it's probably excellent. Stuff that Julianne does used to be excellent.
I don't think the issues with printing are to bad, modern printers have nice gamuts and at least glossy and luster papers have a wide tonal range. Perceptual rendering intent fixes minor issues. If you cannot see colors on screen, you should probably sort out the issue on screen.
One question here is, does gamut apply to the sensor or does gamut only apply to the output medium (be it a monitor or printer/paper)?
The other question is more basic - is there any way for LR or anything else to tell me when a pixel (or two or three) is out of the gamut range of my monitor?