Taking into account the recent progress in the understanding of the lepton flavour effects in leptogenesis, we investigate in detail the possibility that the CP-violation necessary for the generation of the baryon asymmetry of the Universe is due exclusively to the Dirac and/or Majorana CP-violating phases in the PMNS neutrino mixing matrix $U$, and thus is directly related to the low energy CP-violation in the lepton sector (e.g., in neutrino oscillations, etc.). We first derive the conditions of CP-invariance of the neutrino Yukawa couplings $\lambda$ in the see-saw Lagrangian, and of the complex orthogonal matrix $R$ in the ``orthogonal'' parametrisation of $\lambda$. We show, e.g. that under certain conditions i) real $R$ and specific CP-conserving values of the Majorana and Dirac phases can imply CP-violation, and ii) purely imaginary $R$ does not necessarily imply breaking of CP-symmetry. We study in detail the case of hierarchical heavy Majorana neutrino mass spectrum, presenting results for three possible types of light neutrino mass spectrum: i) normal hierarchical, ii) inverted hierarchical, and iii) quasi-degenerate. Results in the alternative case of quasi-degenerate in mass heavy Majorana neutrinos, are also derived. The minimal supersymmetric extension of the Standard Theory with right-handed Majorana neutrinos and see-saw mechanism of neutrino mass generation is discussed as well. We illustrate the possible correlations between the baryon asymmetry of the Universe and i) the rephasing invariant $J_{\rm CP}$ controling the magnitude of CP-violation in neutrino oscillations, or ii) the effective Majorana mass in neutrinoless double beta decay, in the cases when the only source of CP-violation is respectively the Dirac or the Majorana phases in the neutrino mixing matrix.