The Black Moon reinforces the independent and original nature of Uranus. If well aspected to the rest of the chart, it can be an extremely creative aspect.
Black Moon-Lilith and Uranus have a number of features in common: taste for independence, dislike of routines and anything which can perceived as enslaving constraints, affinity with original things, and a rebel (if not rebellious) nature. (In Kabbalistic mythology, Lilith was Adam's first wife. She rebelled and left him because she did not want to be subjected to his control.)
On the lower mode, a major Uranus-Black Moon aspect can enhance the potential restlessness
associated with Uranus and make it difficult for the native to stick to long term enterprises or follow any kind of discipline.
On the higher mode, the sharpness and originality of Black Moon will reinforce the imagination and creativity of Uranus.
On an even higher mode, the metaphysical depth of the Black Moon combines with Uranus in the chart of great visionaries such as Sri Aurobindo (Mars, Uranus, Black Moon conjunct in the 12th), or Edgar Cayce (opposition). Think also of the depth of vision of people such as John Kennedy (opposition), or Steven Spielberg (opposition).