The present understanding of asymmetric lamellar eutectics focuses on pure diffusive transport, and how the external perturbations cause asymmetric pattern transitions remains unclear. In this work, the effect of external perturbations is discussed in terms of both thermal and convective effects via phase-field modeling. The presence of thermal perturbation distorts eutectic lamellae, while the convective perturbation causes a tilt band. Both can adjust the eutectic trajectory to accommodate newly established thermodynamics by reconstructing the transport equilibrium. Furthermore, how to regulate the eutectic growth (eutectic colony, zigzag, and snakelike patterns) by altering external perturbations is investigated, which provides information on how to control eutectic evolution.