  We consider a type-I seesaw framework with a flavour symmetry from the series
of non-abelian groups $\Delta (3 n^2)$ and $\Delta (6 n^2)$ and a CP symmetry.
Breaking these symmetries non-trivially results in the right-handed neutrinos
being degenerate in mass up to possible (further symmetry-breaking) splittings
$\kappa$ and $\lambda$, while the neutrino Yukawa coupling matrix encodes the
entire flavour structure in the neutrino sector. For a fixed combination of
flavour and CP symmetry and residual groups, this matrix has five real free
parameters. Four of them are set by light neutrino masses and data on lepton
mixing, while $\theta_R$ is related to right-handed neutrinos. We scrutinise
for all four lepton mixing patterns, grouped into Case 1) through Case 3 b.1),
the potential to generate the baryon asymmetry of the Universe (BAU) through
low-scale leptogenesis numerically and analytically. The main results are: a)
the possible correlation of the BAU and the Majorana phases of the PMNS mixing
matrix in certain instances; b) the possibility to generate the correct amount
of BAU for zero $\kappa$ and $\lambda$ as well as for large $\kappa$, depending
on the case and choice of group theory parameters; c) the chance to produce
sufficient BAU for large active-sterile mixing angles, enabling direct
experimental tests at current and future facilities, for $\theta_R$ close to a
special value, potentially protected by an enhanced residual symmetry. We
elucidate these results with representative examples of flavour and CP
symmetries, which all lead to a good agreement with the measured lepton mixing
angles and, possibly, the current hint of the CP phase $\delta$. We identify
the CP-violating combinations relevant for low-scale leptogenesis, and show
that the parametric dependence of the BAU found numerically can be understood
well with their help.
