It can be very surprising where people will put pets, like an alligator, when they don't want them anymore.
As I recall Lake Michigan is a darn cold lake in some areas....too cold for alligators....it would have probably died anyway. I'm sure there are some warmer parts of it but Illinois and Michigan aren't those areas. As a child I remember going to Indiana to swim in Lake Michigan there...seemed warmer.
Yeah, it certainly wouldn't have survived the winter, which is coming anytime now. My brother, who still lives in my hometown, said there was already snow an hour north of there.
I can attest to the fact that Lake Michigan is DARNED cold, for the major part of the year. By the time I was in the 7th. grade, it's level of pollution had reached such extremes, that I got a major inner ear infection from swimming in it, on the Michigan side, at that. After heavy rain, the Chicago River, into which 4 million or so toilets drain, was reversed so that it emptied into the lake, diverted from it's normal outlet, the Northern Illinois Waterway, otherwise known as the Illinois Sanitary and Ship Canal, which we lovingly called the "shit canal". Pictures taken from the air showed an enormous "slug" of waste flowing outward into the lake several miles. The "water cribs" from which the City and many suburbs received domestic water were one mile out. Such disgusting events prompted me to leave my birthplace. Sorry, devout Chicagoans! Sorry, Charlie! we "be gone"! Frank
Someone probably got it as an "exotic" pet and then found it was to much trouble so they dumped it in the lake.