I must be missing something here - you're John Deere LT160 has a cooling fan? I thought those mowers had the single-cylinder Kohler air-cooled engine. Did they produce some with water cooling?

My best guess is the starter motor continued to run. Stuck solenoid etc. There isn't actually an electrical cooling fan, but I could see where it could sound that way. If you reconnect the battery, the starter may not run up w/o turning the key- but it could occur again.

In which case, it would mean your starter solenoid is "sticking".

Forrest Gump Syndrome.

Forrest Gump Syndrome.

Thanks to all for the responses to my problem. Don't understand Mownie's advice.

That's because it was a comment.
Forest Gump ran & ran & ran.....

Forrest Gump kept running too.
I believe tomplum nailed what you were hearing.
Bill Kapaun ID'd the cause.
That left room for me to attempt a weak pun.
:^)