Cpurvis has probably nailed it.
You do not damage an engine by tipping it up when it is not running.
I have a yard hoise and usually lift most mowers near vertical when working under them.
However a few precautions are necessary like removing batteries and clamping off fuel lines so they can not drain down into the engine.
Even then the oil inside the engine can drain back where it should not be & cause grief.
So do as previously advised.
Also check the oil.
If the level is higher than it should be or feels thin or smells like fuel then change it as fuel has drained into the sump and will be diluting the oil.
Also make sure that the spark plugs are well out of the way because if the cylinder is full of fuel , on a hot day you can get a really cool flame thrower when you crank the engine.