Inherited disease is not one of Lamark's ideas, iirc, any more than congenital syphilis.
My point, for clarification, is that is more likely that exposure to a pathogen would be an environmental pressure that selected genetic mutations that favored survivability rather than a direct instigator of the genetic change itself.
Kinda just borrowing your Occam's Razor to split hairs, so to speak.
You are a little off regarding inherited diseases, however. Something such as congenital syphilis is not genetically inherited. Rather, it is a result of the child being directly infected in utero. Remove the pathogen and future progeny won't be infected. Other heritable maladies, such as sickle cell anemia, actually are a genetic predisposition that is passed on to future generations. These, however, are genetic defects, not pathogenic infections.
Out of interest, how many diseases must the passengers on the ark have been carrying? Given that we are supposedly all descended from them, and that those who believe in the ark tend to deny large-scale evolution... ;)