The B-spline configuration-interaction method is applied into the investigations of dynamic dipole polarizabilities for the four lowest triplet states (^{2}3S, ^{3}3S, ^{2}3P, and ^{3}3P) of the Li^{+} ion. The accurate energies for the triplet states of n^{3}S, n^{3}P, and n^{3}D, the dipole oscillator strengths for ^{2}3S(^{3}3S)→n^{3}P, ^{2}3P(^{3}3P)→n^{3}S, and ^{2}3P(^{3}3P)→n^{3}D transitions, with the main quantum number n up to 10 are tabulated for references. The dynamic dipole polarizabilities for the four triplet states under a wide range of photon energy are also listed, which provide input data for analyzing the Stark shift of Li^{+} ion. Furthermore, the tune-out wavelengths in the range from 100 nm to 1.2 μm for the four triplet states, and the magic wavelengths in the range from 100 nm to 600 nm for the ^{2}3S→^{3}3S, ^{2}3S→^{2}3P, and ^{2}3S→^{3}3P transitions are determined accurately for the experimental design of the Li^{+} ion.