Let's see where to start.
Lightroom is a raw processor at heart. You can import and adjust JPG images but their colorspace will not be altered.
G10 can record either RAW (CR2) or processed JPG files, or both. To get the most out of your G10 with LR - shoot RAW... maybe.
RAW files have no colorspace, the image files created from a RAW file will have a colorspace applied. The JPGs from the G10 may be sRGB ( I have a G10 and I don't know, I always shoot RAW)
The ProPhoto Working Colorspace of LR isn't a concern, its simply elbow room to work in. To create an image file from the RAW file and the LR adjustments/processsing, the image must be exported from LR. The export process will ask you to determine the image colorspace to be applied. Depending on the ultimate destination for the image, choose appropriately.
Now back to the ... Maybe. If your G10 is a point and shoot JPG camera that you want to simply off load images and send around to your friends then LR is probably overkill. If you are a RAW (or a serious JPG) shooter and want to learn the idiosyncrasies of the digital imaging world and all of the color management possibilities and frustrations, LR may be for you.
You may want to try these questions in the beginners section, or at least the LR section, of the forum. You've stumbled on to a very high end forum (I'm typically a lurker here grasping what I can from these folks) and these questions will a lot of times go unanswered.
Thanks a lot!
Your explanation is clear and helped me. BTW, I shoot RAW only.