Muon spin rotation/relaxation (μSR) and specific heat measurements are presented for polycrystalline LnCuGa₃, with Ln = La-Nd, and Sm-Gd. All materials undergo magnetic ordering transitions, apart from non-magnetic LaCuGa₃, and PrCuGa₃, which shows the onset of short range correlations below 3 K but no long-range magnetic order down to T = 25 mK. While magnetic order in the Ce and Nd compounds is incommensurate with the lattice, the order is commensurate for the Sm and Eu compounds. The strong damping in GdCuGa₃ prevents us from determining the nature of magnetism in that system. SmCuGa₃ exhibits two precessional frequencies, which appear at different temperatures, suggesting inhomogeneous magnetic ordering or a second magnetic/structural phase transition.