It seems that the expressions for Log pointwise posterior predictive density (LPPD) and posterior predictive checks (PPC) are similar (except for the log computation).
Is it possible to calculate LPPD using PPC?
Yes, the posterior predictive distribution is the relevant distribution in both of these cases. See the bottom of page two of this paper:
https://arxiv.org/abs/1507.04544
Each term in the sum for lpd is just the the log of the posterior predictive density evaluated at one of the data points.