Step 1: LHON is the classic mitochondrial inheritance disorder of the optic nerve. The single most important fact is that mitochondria come only from the egg, hence the inheritance is purely maternal.
Step 2: Apply that to each option. A male, even if affected, contributes sperm whose mitochondria are not passed to the offspring, so he is a genetic dead end for this trait. The statement that males can transmit the disease therefore contradicts the basic biology and is the EXCEPTION being asked for.
Step 3: Verifying the rest: onset is in the young adult years (roughly 11 to 30, the 2nd-3rd decade) [true]; the visual failure is subacute and painless, matching a gradual painless loss [true]; and although the acute disc looks swollen with peripapillary telangiectasia, dye does NOT leak from the disc on fluorescein angiography [true].
Step 4: The one false statement is male transmission.
\[\boxed{\text{Males can transmit the disease}}\]