In this study, we characterize $LP$-Kenmotsu manifolds admitting $\ast$-Ricci–Yamabe solitons ( $\ast$-RYSs) and gradient $\ast$-Ricci–Yamabe solitons (gradient $\ast$-RYSs). It is shown that an $LP$-Kenmotsu manifold of dimension $n$ admitting a $\ast$-Ricci–Yamabe soliton obeys Poisson's equation. We also determine the necessary and sufficient conditions under which the Laplace equation is satisfied by $LP$-Kenmotsu manifolds. Finally, by using a non-trivial example of an $LP$-Kenmotsu manifold, we verify some results of our paper.