With gas and oil in the mower, the only secure way to tip one over for service is so the LEFT wheels are up, and the RIGHT wheels remain down. Tipping in any other position will run the risk of oil/fuel draining into into the "wrong" parts of the engine or onto the ground. What a mess!
Here's a photo showing the proper tip-over for an oil change:
An alternative to get at all four wheels for removal, cleaning, greasing, etc. would be to position the mower onto a pair of square lengths of lumber under the deck, like a set of jack stands on a car. This would keep the mower level and avoid any draining problems.
And I always instruct customers to tip the mower back and pop a brick on the handle.
Most mowers will sit upright if you undo the handle clamps.
As for oil changing, I use a pump and try to sell them to customers.
Women buy them men won't.
Picking up a hot mower and tipping it over to change the oil is a lot more dangerous to the operator than using the mower.