Central Florida's climate divides neatly into a hot wet season (June through September) and a warm dry season (October through May). For visiting Leesburg, the dry season is clearly preferable — temperatures are comfortable (low 20s Celsius by day), the mosquitoes are manageable, and the lakes are at their most attractive for fishing and boating.
April brings Bikefest, which is either a reason to come or a reason to stay away depending on your taste for large motorcycle rallies. If you are coming for the lakes and nature, February through April is the sweet spot: birdwatching is excellent, the weather is reliably pleasant, and the town is not yet fully into summer torpor.
Summer (June through August) is hot and humid with afternoon thunderstorms most days. The lakes are still usable in the mornings but midday heat is oppressive. Hurricane season runs June through November, though Leesburg's inland location means it is less exposed than the coasts.