We have developed a significantly more flexible variant of the relativistic atomic method of calculation that combines configuration-interaction and coupled-cluster approaches. The new version is no longer restricted to a specific choice of the initial approximation corresponding to the self-consistent field of the atomic core. We have applied this approach to calculation of different properties of atomic lead, including the energy levels, hyperfine structure constants, electric-dipole transition amplitudes, and E1 parity nonconserving (PNC) amplitude for the 6p(2) P-3(0) -6p(2) P-3(1) transition. The uncertainty of the E1 PNC amplitude was reduced by a factor of two in comparison with the previous most accurate calculation [V. A. Dzuba et al., Europhys. Lett. 7, 413 (1988)]. Our value for the weak charge Q(W) = -117(5) is in agreement with the standard-model prediction.