The dilute lamellar phase of the nonionic surfactant C12EO5 was doped with goethite (iron oxide) nanorods Lip to a fraction of 5 vol %. The interaction between the inclusions and the host phase was studied by polarized optical microscopy (with or without all applied magnetic field) and by small-angle X-ray scattering. We find that, when the orientation of the nanorods is modified using the magnetic field, the texture of the lamellar phase changes accordingly; one can thus induce a homeotropic-planar reorientation transition. On the other hand, the lamellar phase induces all attractive interaction between the nanorods. In more concentrated lamellar phases (under stronger confinement) the particles form aggregates. This behavior is not encountered for a similar system doped with spherical particles, emphasizing the role of particle shape in the interaction between doping particles and the host phase.