I have some plastic oil containers that have the caps tightened but left in an unheated WI garage. Is it still good for the lawnmower?
Assuming that the oil is the right viscosity for the lawnmower and has the correct service rating, you should be fine. Keep in mind that many small air cooled engines should use a straight 30 weight oil in the summer and the oil should be heavy detergent.
Old oil doesn’t degrade like gasoline. Standards improve, so it could be ‘obsolete’ for a newer car, but not because it’s in bad shape.
Crude oil is already millions of years old when it’s brought to the surface. A few years on the shelf won’t make any difference.
It should be fine. I’ve got some 25 year old Harley Davidson motor oil that is still fine although the 25+ year old Harley Davidson Commemorative six-packs of beer I have are probably not.