At the same time the designation 'lady of Hallabi' points to her being a consort of a male deity who was the patron of the place.

May this have been the moon-god again, as in the case of the other Innanna?
Our knowledge of this goddess is confined to what the king tells us about her.

For him she is the mistress whose glory fills heaven and earth, but when he adds that she has placed in his hands the reins of government, this only means that the goddess recognizes his right to supreme authority over the Babylonian states--not that he owes his power to her.
It is after he has succeeded in making Babylon the capital of a great kingdom that he proceeds to improve the temple of Innanna.
Bel and the Triad of Babylonian Theology.
Among the literary remains of Hammurabi's days we have a hymn in which the chief gods worshipped by the king are enumerated in succession.

The list begins with Bel, and then mentions Sin, Ninib, Ishtar, Shamash, and Ramman.

We should expect to find at the head of the list Marduk.