  We consider the time evolution of local observables after an interaction
quench in the repulsive Lieb-Liniger model. The system is initialized in the
ground state for vanishing interaction and then time-evolved with the
Lieb-Liniger Hamiltonian for large, finite interacting strength $c$. We employ
the Quench Action approach to express the full time evolution of local
observables in terms of sums over energy eigenstates and then derive the
leading terms of a $1/c$ expansion for several one and two-point functions as a
function of time $t > 0$ after the quantum quench. We observe delicate
cancellations of contributions to the spectral sums that depend on the details
of the choice of representative state in the Quench Action approach and our
final results are independent of this choice. Our results provide a highly
non-trivial confirmation of the typicality assumptions underlying the Quench
Action approach.
