  In this article, we are interested in the strong well-posedness together with
the numerical approximation of some one-dimensional stochastic differential
equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a
spectrally-positive L{\'e}vy process and a Brownian motion. We provide criteria
for the existence of strong solutions under non-Lipschitz conditions of
Yamada-Watanabe type without non-degeneracy assumption. The strong convergence
rate of the propagation of chaos for the associated particle system and of the
corresponding Euler-Maruyama scheme are also investigated. In particular, the
strong convergence rate of the Euler-Maruyama scheme exhibits an interplay
between the regularity of the coefficients and the order of singularity of the
L{\'e}vy measure around zero.
