  We introduce a generic algorithm to determine the time delays and spacecraft
(S/C) positions to compose any time-delay interferometry (TDI) channel in the
dynamical case and evaluate its sensitivity by using a full numerical method.
We select 11 second-generation TDI channels constructed from four approaches
and investigate their gravitational wave responses, noise levels, and averaged
sensitivities under a numerical LISA orbit. The sensitivities of selected
channels are various especially for frequencies lower than 20 mHz. The optimal
channel A$_2$ (or equivalently E$_2$) combined from second-generation Michelson
TDI channels (X$_1$, X$_2$, and X$_3$) achieves the best sensitivity among the
channels, while the Sagnac $\alpha_1$ channel shows the worse sensitivity.
Multiple channels show better sensitivities at some characteristic frequencies
compared to the fiducial X$_1$ channel. The joint $\mathrm{A_2+E_2+T_2}$
observation not only enhances the sensitivity of the X$_1$ channel by a factor
of $\sqrt{2}$ to 2 but also improves the capacity of sky coverage.
