Forget about Lumens, just look at the wattage of the bulb. With those screw in LEDs (SIL) you should only need about 35-watts per square foot. My filing cabinet was only 86-watts.
Forget CFL, they are old technology. The SIL are not only more efficient, but also have a better light distribution. They also run cooler. I’m not really a fan of those purple lights. If it were me, I would run three 14-watt LEDs in any spectrum and ditch the purple light in the side.
You’re definitely going to need a speed controller for that fan, a 4" fan on full blast sounds like a jet engine.