I got this mower with the house I purchased. I really like it. I have to change the oil, but I don't see a drain plug. Do I just flip it over and drain it thorugh the fill, or am I missing something?

I am not finding that particular mower, can you find additional model or serial numbers. Some have a plug on the underside of the mower just above the blade, others pour out a side square bolt, none have to be turned upside down.

Yes just lay it on the side and put something under the fill tube.
When then unit was new it probably came with a drain tube.