If it has the muffler under the deck, it's most likely fuel mix coming out of the muffler after it leaked into the engine from the carburetor.
Temporary fix; install a fuel shut-off valve on the fuel line from the tank, and close it when you're through with the mower.
Correct fix; overhaul carburetor.

You could also have a second problem, a leaking fuel tank, common on Lawn-Boys.

rob123, saxman1 is right, Lawn Boys are known for their carbs leaking through the engine and out the muffler when left sitting overnight or longer. The fix is to remove and clean the carb and install a new float and inlet valve assembly, then install an inline fuel shutoff valve. Might as well install an inline fuel filter also, they keep the carb clean which can lead to a sticking inlet valve. The manual says to put a drop of locktite on the inlet valve threads and the main nozzel threads to seal them also don't over tighten the carb mounting screws. With these mods you should be set to go.

Thanks for the advice. I think I'll try to get through the rest of the mowing season with it and the fuel cutoff. Once the season is over I'll rebuild the carb... Thanks again.

Truth is. If underneath the transmission. It's the fuel shut off kit underneath the tank itself. I own an 8125. Had the same issue. Just ordered a new one off of ereplacemwntparts.com for 21 dollars. As they built the d and F series engines with them built into the shroud tank. As they use a gravity feed fuel system that is returnless. And they have a fuel filter on the carburetor. If you notice that lever on the bottom of most 80's plastic shroud tank lawnboys. They utilize a gravity feed returnless fuel system as epa rules weren't big in the 80's. So they used a returnless system with plastic carburetor. So they made the shut off kit stock on them to shut off the fuel when not in use as well as an easy way to remove the tank from the mower without making a mess as they were built into the shroud. So check that for leaks first as it's an easy fix.

Green color fluid is just the color of your gas with certain brands of 2-cycle oil mix. The gas evaporates and leaves the oil. I am not aware of any Lawnboy transmission that has anything but thick grease in it, and that would never "puddle" under the mower.