The effect of surfactant bilayer arrangement on the swelling and dissolution of a bulk lamellar phase is studied by optical microscopy in penetration-scan experiments, on an AOT/brine system. Contact experiments with powder lamellar samples show classical myelin figures, as expected for systems with a wide L-alpha/L-1 miscibility gap, although a sponge phase (L-3) also forms at the interface, whose role is discussed. By shearing the lamellar phase prior to contact, we prepare a metastable state of close-packed multilamellar vesicles (the onion phase). Myelin features are strongly suppressed in contact experiments using the onion phase. The dissolution processes for onions, which depend on the onion size, are interpreted in terms of the equilibrium phase behavior of the system and the size-dependent stability of the onion phase. When onions dissolve to join the L-3 phase, we observe two remarkable features: (a) a "raspberry-like" texture at the surface of the LQ phase, suggesting that this is initially formed as an emulsion of discrete droplets; (b) the expulsion of small unswollen remnants or "onion cores" from the sponge phase as onions merge with it.