AbstractGiven a metrizable locally convex-solid Riesz space of measurable functions we provide a procedure to construct a minimal Fréchet (function) lattice containing it, called its Fatou completion. As an application, we obtain that the Fatou completion of the space L¹(ν) of integrable functions with respect to a Fréchet-space-valued measure ν is the space L¹_w(ν) of scalarly ν-integrable functions. Further consequences are also given.