Very few ceiling fans come with LED lights because they are currently far more expensive than other lighting options and most fan manufacturers want to keep their fans in a somewhat competitive price range. If you are trying to keep bugs out of the light fixture, then you more than likely need a fixture that is enclosed rather than an open bowl. So this limits your choices even more since some of the LED light fixtures available are in fact open bowls.
The only good quality fan I am aware of that comes with an enclosed LED light fixture is the Landan ceiling fan made by Fanimation, which sells for $599.00. Quite pricey, but is does represent the latest state-of-the-art technology for ceiling fans and is considered an eco-friendly fan. Not only does it have a fully enclosed LED light, it also has a super efficient DC fan motor with a 6 speed remote control that has a light dimmer and reverse function. DC motors use 3 to 5 times less electricity than standard fan motors, yet produce better airflow.
The DC motor in the Fanimation Landan uses only 29.5 Watts yet produces over 6,100 CFM of airflow where the average ceiling fan uses closer to 75 watts and produces about 4,000 to 5,000 CFM. The LED lights in the Landan use only 15 watts where typical fan lights use between 60 and 190 watts.
Use the links below to view the Landan as well as other fans with LED lights.