This is a Congressional map. Nobody in this lawsuit is trying to flip the state legislature. They are trying to enforce the Voting Rights Act, which is about race not party affiliation.
According to the SCOTUS, the number of Black-majority Alabama districts should be proportional to the number of Blacks in Alabama. Alabama has seven Congressional representatives, of whom one is Black. The state is roughly one quarter Black, so the goal of the lawsuit is to make sure it has two Black-majority districts in Congress. Nothing more. The other five will surely be Republican-controlled, and everyone knows that the courts cannot change that. Two out of seven is our best-case scenario, for now at least.
Other lawsuits have tried to force various maps, at the state and congressional level, to match the number of Democratic-leaning districts to the proportion of Democrats in the state. Any such efforts have no support from the SCOTUS and no chance of success in Alabama.