I choose to oil the fingerboard and bridge of the guitars that I own, and those that I build. I find that it adds to the look of the instrument, and less so but still relevant, the feel. This is purely opinion/personal. I use a 33/66 mineral oil/beeswax mixture and use it very sparingly (almost as a polish). Mineral oil = lemon oil and I have used mineral oil in the past.
I've never had a fretboard dry out to the point that oil would have saved it, but I keep my guitars humidified and taken care of. If your fingerboard is cracking, it's either 1) ebony or 2) so dry that the top has already cracked.
1) Ebony (or blackwood or other esoteric/exotic) fingerboards tend to be less stable than rosewood/maple. That being said, if you own a guitar with an ebony fingerboard (they are expensive nowadays), then you likely paid enough that you're going to humidify/care for your guitar.
2) A solid spruce top guitar will crack at the top due to dryness far before the fingerboard cracks from the same factors. If you let it get to the point where the fingerboard (rosewood/maple) also cracks, you likely have damage that is irreparable simply with oil. A luthier will have to fix it. I would hope one would notice and take the guitar for repair/advise before this point.