I haven't run into HOMO and LUMO levels of fluorescein in the literature. It may be. But I advice using the Cyclic voltammetry method. You can find some articles in the literature regarding on this matter. For instance, RSC Adv., 2015, 5, 18710–18719.
A simple HF/6-31G* or B3LYP/6-31G* calculation with any quantum-chemistry package available will print the H and L shapes and energies. Is that what you want?
well then, good luck... you won't find it anywhere in this world...
it comes as calculated parameter from quantum chemistry based on abstract, simplified models; and there is a huge gap between this and the world of measurements...
see this paper please. It is free and can be downloaded and read on computer:
The ground state geometry of both molecules were opti-mized using GGA/PBE 6-31G (d,p) basis sets [13], fromthis calculations we obtained, the highest occupied molecu-lar orbital HOMO) and the lowest unoccupied molecular orbital (LUMO) distributions. The optimized geometries for dabcyl and fluorescein are shown in Fig.1.