Your doing it right, just check the latest oil you removed to see if there is any gas residue still coming out. Make sure you remove spark plug to make it easier to turn engine over w/o starting.
Don't know what type of mower you are talking about, but does it have an oil filter that would need to be changed. These are normally only on much larger engines(riders) or commercial walk-behind units, but thought I'd throw that out there just in case.
When you first start it up, listen closely for any strange noises or rough running.
-If it sounds OK, I'd suggest running for 3 to 5 minutes to let entire engine block get warm without actually using it for work(under load), then change the oil one last time to make sure all internal oil passages are cleaned out.
-If strange noises, you can redo your prior steps again and hope.
And lastly, did you check the gas tank to make sure she didn't put oil in there?!?
Sorry, but if so: drain & clean tank(oil will sit on bottom), check gas line filter and install new spark plug.
These (and most) engines allow some blowby past piston rings...that's why the oil gets darker. But these crude little engines normally can take quite some abuse by the average owner.