Hi!
I love the Lily-gorgeous bag!
All are good versatile colours, but slightly different I think. The black can come with either silver or gold hardware if that interests you? (it was a deciding factor for me when making a decision on colour of Lily!) I believe the black is also glossy goat, and the oak and the oxblood are different materials too. Oak is the natural leather but the oxblood is natural grain (new leather), although you might be able to get the oxblood in natural leather still. Obviously I am assuming you are buying new not preloved, which might alter your decision too!
Otherwise, what colour would you wear most? The black and oxblood are maybe more dressy, whereas the oak more casual, but I personally think you could wear all for most occasions!
Sorry, more of a stream of thoughts rather than an actual answer! I hope someone more decisive than me will be along soon to help!