An updated one-dimensional two-layer coupled mathematical model is developed for landslide generated impulse wave (LGIW) from wave formation to long-duration travel. The coupled model is composed of a landslide model in a bed-fitted coordinate system and a shallow-water wave model in a global coordinate system. The coupling is realized through a reconstruction and interpolation algorithm. We successfully reproduced the experimental reproduction of 1958 Lituya LGIW for a total duration of 250 s at prototype scale, and well captured the three runups on the right bank and three runups on the left bank, together with the six wave crests and troughs in the channel. This seems to be the first reproduction of the Lituya LGIW for such a long duration. The predicted free surface elevation and runups are comparable with experimental results though with some deviations. However, the level of reproduction of the Lituya LGIW from wave formation to long-duration traveling achieved by numerical simulation is greatly enhanced as compared with the existing interface-capture models and mesh-free/particle-based models. This proposed one-dimensional two-layer coupled model could provide a unified framework for LGIWs from generation to long-duration propagation.