This article proposes a test of stationarity for random fields on a regular lattice motivated by a problem arising from texture analysis. Our approach is founded on the locally stationary two-dimensional wavelet (LS2W) process model for lattice processes which has previously been used for standard texture analysis tasks such as texture discrimination and classification. We propose two variants of our stationarity test, both of which can be performed on a single realisation – a feature of particular practical importance within texture analysis. We illustrate our approach with pilled fabric data, demonstrating that the test is capable of identifying visually-subtle changes in stationarity. Supplementary material for this article is available online.