measurements are highly motivated for addressing lepton-flavor-universality(LFU)-violating puzzles such as anomalies. The anomalies of and further strengthen their necessarity and significance, given that the LFU-violating hints from both involve the third-generation leptons directly. factories of future colliders stand at a great position to conduct such measurements, because of their relatively high production rates and reconstruction efficiency for mesons at pole. To fully explore this issue, we pursue a sensitivity study for four benchmark channels, namely, , , and , at the future factories. A scheme of -meson reconstruction mainly based on detector tracking system is developed for this purpose. The simulations indicate that at Tera- the branching ratios of the first three channels can be measured with a precision of and that of with a precision of . The interpretation of these results in effective field theory is presented.