Autonomous vehicles need to plan trajectories to a specific goal while avoiding collisions with surrounding vehicles. To this aim, it is essential to take into account the inherited uncertainties due to unmodeled dynamics, uncertain localization, and disturbances. This paper deals with the problem of robust trajectory planning for autonomous lane-changing in the presence of uncertainties. Considering trajectory planning as an online decision-making problem, we propose a robust model predictive control (rMPC), which minimizes deviations from a reference speed and a lateral target position while keeping a subject vehicle within road limits and avoiding collisions with an in-lane vehicle. Uncertainties are explicitly modeled as an additive disturbance in the formulation, wherein the optimal control decisions are obtained by solving a quadratic program (QP). The resulting rMPC guarantees robust state-input satisfaction under the additive disturbance even when the QP solver iterations are stopped prematurely. A set of simulation experiments is studied under different initial scenarios to validate the design, demonstrating the potential utility of the proposed control algorithm for reliable lane-changing.