Fast concentration-induced diffusion-limited lyotropic phase transitions can be studied in situ with millisecond time resolution using continuous flow microfluidics in combination with microfocus small-angle X-ray scattering. The method was applied to follow a classical self-assembly sequence where amphiphiles assemble into micelles, which subsequently assemble into an ordered lattice via a disorder/order transition. As a model system we selected the self-assembly of an amphiphilic block copolymer induced by the addition of a nonsolvent. Using microchannel hydrodynamic flow-focusing, large concentration gradients can be generated, leading to a deep quench from the miscible to the microphase-separated state. Within milliseconds the block copolymers assembly via a spinodal microphase separation into micelles, followed by a disorder/order transition into an FCC liquid-crystalline phase with late-stage domain growth and shear-induced domain orientation into a mesocrystal. A comparison with a slow macroscopic near-equilibrium kinetic experiment shows that the fast structural transitions follow a direct pathway to the equilibrium structure without the trapping of metastable states.