In this work we present a systematic study on the microstructure of soft materials which combine the anisotropy of lyotropic liquid crystals with the mechanical stability of a physical gel. Systematic small-angle neutron (SANS) and X-ray (SAXS) scattering experiments were successfully used to characterize the lyotropic lamellar phase (Lα) of the system D2O -n-decanol - SDS which was gelled by two low molecular weight organogelators, 1,3:2,4-dibenzylidene-d-sorbitol (DBS) and 12-hydroxyoctadecanoic acid (12-HOA). Surprisingly, a pronounced shoulder appeared in the scattering curves of the lamellar phase gelled with 12-HOA, whereas the curves of the DBS-gelled Lα phase remained almost unchanged compared to the ones of the gelator-free Lα phase. The appearance of this additional shoulder strongly indicates the formation of a synergistic structure, which neither exists in the gelator-free Lα phase nor in the isotropic binary gel. By comparing the thicknesses of the 12-HOA (25-30 nm) and DBS (4-8 nm) gel fibers with the lamellar repeat distance (7.5 nm), we suggest that the synergistic structure originates from the minimization of the elastic free energy of the lamellar phase. In the case of 12-HOA, where the fiber diameter is significantly larger than the lamellar repeat distance, energetically unfavored layer ends can be prevented, when the layers cylindrically enclose the gel fibers. Interestingly, such structures mimic similar schemes found in neural cells, where axons are surrounded by lamellar myelin sheets.