We show that, for function f on [0, 1], with ∫ | f| (log log+ |f|)(log log log+ |f|) dx < ∞, and lacunary subsequence of integers {nj}, it holds that S n j f → f a.e., where Smf is the mth Walsh–Fourier partial sum of f. According to a result of Konyagin, the sharp integrability condition would not have the triple-log term in it. The method of proof uses four ingredients, (1) analysis on the Walsh Phase Plane, (2) the new multi-frequency Calderón–Zygmund Decomposition of Nazarov–Oberlin–Thiele, (3) a classical inequality of Zygmund, giving an improvement in the Hausdorff–Young inequality for lacunary subsequences of integers, and (4) the extrapolation method of Carro–Martín, which generalizes the work of Antonov and Arias-de-Reyna.