We investigate the double spin asymmetries of pion production in semi-inclusive deep inelastic scattering with a longitudinal polarized beam off a transversely polarized proton target. Particularly, we consider the cos phi(s) and cos(2 phi(h) - phi(s)) modulations, which can be interpreted by the convolution of the twist-3 transverse momentum dependent distributions and twist-2 fragmentation functions. Three different origins are taken into account simultaneously for each asymmetry: the g(T)D(1) term, the e(T)H(1)(perpendicular to) term, and the e(T)(perpendicular to)H(1)(perpendicular to) term in the cos phi(s) asymmetry; and the g(T)(perpendicular to)D(1) term, the e(T)H(1)(perpendicular to) term, and the e(T)(perpendicular to)H(1)(perpendicular to) term in the cos(2 phi(h) - phi(s)) asymmetry. We calculate the four twist-3 distributions g(T)(x, k(T)(2)), g(T)(perpendicular to)(x, k(T)(2)), e(T)(x, k(T)(2)) and e(T)(perpendicular to)(x, k(T)(2)) in a spectator-diquark model including vector diquarks. Then we predict the two corresponding asymmetries for charged and neutral pions at the kinematics of HERMES, JLab, and COMPASS for the first time. The numerical estimates indicate that the two different angular-dependence asymmetries are sizable by several percent at HERMES and JLab, and the cos phi(s) asymmetry has a strong dependence on the Bjorken x. Our predictions also show that the dominant contribution to the cos phi(s) asymmetry comes from the g(T)D(1) term, while the g(T)(perpendicular to)D(1) term gives the main contribution to the cos(2 phi(h) - phi(s)) asymmetry; the other two T-odd terms almost give negligible contributions. In particular, the cos(2 phi(h) - phi(s)) asymmetry provides a unique opportunity to probe the distribution g(T)(perpendicular to).