Vacuum solutions of Lovelock gravity in the presence of a recurrent null vector field (a subset of Kundt spacetimes) are studied. We first discuss the general field equations, which constrain both the base space and the profile functions. While choosing a generic base space puts stronger constraints on the profile, in special cases there also exist solutions containing arbitrary functions (at least for certain values of the coupling constants). These and other properties (such as the pp-waves subclass and the overlap with VSI, CSI and universal spacetimes) are subsequently analyzed in more detail in lower dimensions $n=5,6$ as well as for particular choices of the base manifold. The obtained solutions describe various classes of non-expanding gravitational waves propagating, e.g., in Nariai-like backgrounds $M_2timesSigma_{n-2}$. An appendix contains some results about general (i.e., not necessarily Kundt) Lovelock vacua of Riemann type III/N, and of Weyl and traceless-Ricci type III/N. For example, it is pointed out that for theories admitting a triply degenerate maximally symmetric vacuum, all the (reduced) field equations are satisfied identically, giving rise to large classes of exact solutions.
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