On the condition of electron and LO-phonons strong-coupled, the ground-state energy of polaron has been obtained by using linear combination operator and unitary transformation methods in an asymmetric quantum dot. Quantum transition which causes the changes of the polaron lifetime is occurred in the quantum system due to the electron-phonon interaction and the influence of external temperature effect which is the polaron leap from the ground-state to the first-excited state absorbing a LO-phonon. Numerical calculation is performed and the results show that the ground-state lifetime of polaron increases with increasing the ground-state energy and decreases with increasing the coupling-strength. The ground-state lifetime is extended with the shortening of the temperature. It is also observed that the ground-state lifetime is a decreasing function of the transverse and longitudinal confinement lengths of the quantum dot.