The Split Toning selection tool in Lightroom does not have some colours like gray, brown, black etc... for both highlights and shadows.
Is there a specific reason for this?
While split toning can be applied to colour images, it is typically used to add colour to a B&W image, so the ability to change highlights or shadows to white, black or grey wouldn't really make sense.
If you want to change certain colours in your image to a shade of grey, then you'd use HSL and lower the saturation of that colour.
Shades of grey technically have no hue, so any slider in Lightroom/Photoshop that affects hue would not affect pixels that are grey (white or black). So toning, which affects hue, cannot include greys, since they have no hue.
Not sure about brown. It has hue. I think it is more or less a dark red/orange. So if you set the shadows to a red/orange hue, possibly low saturation, you should get something resembling brown. Note: I've tried this - set Hue to "30" and Saturation to "40" in the Shadows and it did a nice brown sepia tone.