I have seen papers where they use small and large unilameller liposomes (size upto few hundred nanometers). But can we measure fluidity of giant unilameller liposomes (size in few micrometers) using the same dye in fluorescent spectroscopy?
Yes, you can measure the anisotropy of the dye loaded in the vesicles. Order and disorder of the bilayer of the vesicles can be related to the fluidity of the bilayer membrane in vesicles.
For vesicles of radius R, by dynamic light scattering (DLS) at such angle that the transfert vector q is higher larger than 1/R, you directly probe the dynamics of membrane fluctuations. That is probably what you mean by "fluidity"...
As Deepthi said, DPH anisotropy can be used with any lipid bilayer membrane. The only concern in your case could be scattering of light, which will be much higher on larger liposomes and the nanopartcles can also add to it (depending on their material). Since you are using giant liposomes, you may also consider techniques such as fluorescence correlation spectroscopy to characterise the membrane fluidity.
Fluidity refers the "fluid-likeness" of lateral diffusion, i.e. inverse of viscosity. DPH anisotropy reports better on acyl-chain order/disorder that most of the time correlates fairly well with the fluidity, but not always, as exemplified by the cholesterol-induced liquid-ordered phase where the lipids diffuse as in (2D) fluid but are ordered.
If you are putting your GUVs in a cuvette and use fluorometer, then DPH is fine for chain order. If you are using a fluorescence microscope to do anisotropy imaging, you must note that the anisotropy will be strongly dependent of the projection of the membrane. E.g., if you are using DPH-PC (and your should use it) that stays fairly well along the acyl chains and the acyl chains are in a gel phase or otherwise very ordered, then at the top and bottom of the GUV the excitation and emission transition dipole moments will lie in the direction of your lightpath and you will get hardly any signal, and even if you get enough signal, the changes in orientation will all be symmetrical for both excitation polarizations, and your anisotropy is expected to be zero. On the other hands, at the sides of the GUV where the lipid chains and DPH are oriented perpendicular to you light path, you will tend to excite them very well with the excitation light that has polarization along the excitation transition dipole moment, and if the chains are fairly immobile, you will tend to get values close to 1 unlike in cuvette in solution where you would get values close to the maximum value of 0.4. Of course, if the chains were very ordered, and you integrated/averaged the anisotropy signal over the whole GUV surface area, then you would end up close to the value 0.4.
If you are genuinely interested in local variations in fluidity along your GUV bilayer and want to image it, choose a phosphatidylcholine with pyrene attached to the sn-2 acyl chain (often abbreviated PPDPC). Then you can image the excimer/monomer intensity ratio. Here is still the possible problem that it also reports on the local clustering (i.e. signal increases both with increasing rate of diffusion and increasing local mole ferction in the membrane), but this you can see if you are imaging the vesicle.