Right in time before easter, I finished my personal egg cup including a lid.
To fit the lid closing over your type of egg, you should choose the following settings:
d_egg: your eggs diameter + 1 to 2 mm
l_egg: your eggs lentgh + 4 to 5 mm
Have fun with it
The overhang part of the cup needs proper cooling, if you print without support - or it gets weird.
The lid can be printed standing on the spikes without support but you will need proper rim and proper cooling there - or it gets weird.