This paper introduces an adaptive attitude control strategy designed for spacecraft to perform stationkeeping maneuvers within a Sun-Earth L1 halo orbit. The approach begins by translating an impulsive stationkeeping requirement into a desired stationkeeping orientation and maneuver duration. Subsequently, a three-phase execution of the stationkeeping maneuver is described. During these phases, a quadratic Lyapunov function (QLF)-based adaptive attitude control law is employed to orient the spacecraft to the desired stationkeeping attitude, transitioning from an initial Sun-pointing configuration and vice versa. The QLF-based control law is synthesized following the principles of backstepping and model-following neuroadaptive attitude control philosophies. In the presence of parametric inaccuracies, the proposed control law and the weight update rule, effectively approximates the disturbances and adapts the control action to achieve the intended objective. Finally, the effectiveness of the stationkeeping strategy is demonstrated via a six degree-of-freedom numerical simulation.