When you refer to the 'lips' needing 'stronger tones' this relates to an area of the image needing a greater tonal range within that area achieved by adding contrast. This is different to the term toning in black and white photography.
Toning is the name given to a process that adds an even colouration to a black and white photograph. Because the colour is even the image is still monochrome just not black and white any longer. Sepia toning is a popular example of this where a black and white print is given a warmer tone to soften the impact of the original black and white.
The photograph is grey because black and white photographs are not just black or white but all tones of grey in between, referred to as grey scale in digital imaging. Black and White is a misnomer in this sense but can be considered as referring to images that are made up of mixtures of black and white in various proportions in other words anything monochrome from black to white.
Here is a quick edit of your photograph showing what can be achieved by increasing contrast for the mid tones just on the lips:
This was done with Photoshop but similar results can be obtained with GIMP. To achieve this I created two new layers that are copies of the image. On the bottom layer of the two I applied the contrast change to the whole layer. This is done with the image adjustment for shadows/highlights in the image->adjustments menu and increased the mid tone contrast by quite a lot. Then on the top layer I added a layer mask so that only the lips are visible from the contrast altered layer. I overdid the contrast slightly just to give you a good idea what can be achieved you would probably want to play around with the adjustment to get it just right.