We describe a modified microfluidic method for making Giant Unilamellar Vesicles (GUVs) via water/octanol-lipid/water double emulsion droplets. At a high enough lipid concentration we show that the de-wetting of the octanol from these droplets occurs spontaneously (off-chip) without the need to use shear to aid the de-wetting process. The resultant mixture of octanol droplets and GUVs can be separated by making use of the buoyancy of the octanol. A simpler microfluidic device and pump system can be employed and, because of the higher flow-rates and much higher rate of formation of the double emulsion droplets (∼1500 s-1 compared to up to ∼75 s-1), it is easier to make larger numbers of GUVs and larger volumes of solution. Because of the potential for using GUVs that incorporate lyotropic nematic liquid crystals in biosensors we have used this method to make GUVs that incorporate the nematic phases of sunset yellow and disodium chromoglycate. However, the phase behaviour of these lyotropic liquid crystals is quite sensitive to concentration and we found that there is an unexpected spread in the concentration of the contents of the GUVs obtained.