Abstract: [Objective] The formation mechanisms and along-strike expansion patterns of the north–south rift systems that developed since the Miocene are among the key scientific questions in current Tibetan Plateau research, and are crucial for understanding the plateau’s deep lithospheric dynamics. This study focuses on the Lunggar Rift and the Dangre Yongcuo–Xuru Co Rift in the western Lhasa terrane, aiming to constrain the rift initiation timing of their southern segments and to explore the underlying deep-seated geodynamic processes. [Methods] Low-temperature thermochronology was conducted on granite and detrital samples collected from the southern segments of the two rifts using apatite and zircon fission-track analysis. Thermal history modeling was performed with HeFTy software to reconstruct the cooling and exhumation histories. [Results] TFission-track ages are mainly clustered between 12 and 10 Ma. Thermal history modeling reveals a pronounced rapid-cooling event during this period, with cooling rates of ~50 °C/Ma, corresponding to vertical exhumation rates of ~2 km/Ma. Comparison with previously published thermochronologic data from the northern segments indicates broadly synchronous rift activity across strike. Detrital apatite fission-track ages exhibit two prominent peaks at 13.7 Ma and 8.0 Ma, reflecting multiphase exhumation rather than a simple northward or southward propagation trend. [Conclusion] The initiation of the north–south rift systems is primarily controlled by asthenospheric upwelling triggered by the tearing of the subducting Indian lithosphere, and by the vertical buoyancy stresses generated by middle–lower crustal flow. The spatial distribution of rifting does not correlate directly with slab-tear geometries. Instead, the development of these rifts records a fundamental transition from mechanical coupling to decoupling between the upper crust and the underthrusting Indian lithosphere. These findings suggest that traditional models of unidirectional rift propagation should be reconsidered.