The paper presents experimental D (1)Pi state lifetime tau(nu＇J＇) data and develops empirical and ab initio approaches concerning D (1)Pi and B (1)Pi lifetimes, as well as D (1)Pi-X (1)Sigma(+), B (1)Pi-X (1)Sigma(+) and D (1)Pi-A (1)Sigma(+) transition dipole moment functions mu(R) of the NaK molecule. Experimental D (1)Pi (nu＇,J＇), state tau(nu＇J＇) values for nu＇ varying from 1 to 22 have been obtained from experimentally measured electric radio frequency-optical double resonance (rf-ODR) signal contours. The rf-ODR signals have been produced by D (1)Pi<--X(1)Sigma(+) laser induced optical transition and rf field (1-900 MHz) induced e-f transition within the D (1)Pi(nu＇,J＇) level. The possibility to determine empirical absolute mu(R) function in a wide R range from experimental tau(nu＇J＇) dependence on nu＇ and J＇ has been demonstrated; such an approach has been applied to obtain mu(R) for the B (1)Pi-X(1)Sigma(+) transition on which relative intensity data are absent. The empirical D (1)Pi-X(1)Sigma(+) mu(R) function has been considerably improved by simultaneous fitting of relative intensity and lifetime data implicitly accounting for the J＇ dependence of measured lifetime values. The finite-field technique combined with the many-body multipartitioning perturbation theory was used for ab initio all-electron transition moment calculations. This approach appeared to be adequate to compute reliable mu(R) functions due to a proper description of core-valence correlations. As a result, excellent agreement between ab initio and empirical B (1)Pi-X (1)Sigma(+) and D (1)Pi-X (1)Sigma(+) transition dipole moment functions has been achieved.