The origin of Lambda -doubling effect (q factors) for the regularly perturbed NaK B (1)Pi and D (1)Pi states has been investigated by means of ab initio many-body multipartitioning perturbation theory calculation of the electronic L-uncoupling matrix elements between the examined (1)Pi and five lowest (1)Sigma (+) states for both (NaK)-Na-23-K-39 and (NaK)-Na-23-K-41 isotopomers. The hypothesis of pure precession was found to be valid for the B (1)Pi -A (1)Sigma (+) and D (1)Pi -C (1)Sigma (+) pairs of the interacted states, while the unique perturber approximation works properly for the D (1)Pi state and completely breaks down for the B (1)Pi state. The theoretical rovibronic q-factor values estimated for both states by means of the approximate sum rule agree well with their experimental counterparts and demonstrate high sensitivity to vibrational and rotational quantum numbers.