Hi Melissa,
I love both of those shows too and I know how difficult it can be to plan your park days around them. Show times do vary so make sure to pick up a Times Guide (this will list all the show times etc and can be found next to the maps) as you enter the park to get the definite times for your day. For a rough idea I love a site by Steve Soares which can be found
HERE he lists all the show times for the current week so you should be able to get a rough idea before you leave.
For example at the moment Lion King is showing at 10:00 & 11:00am, 12:00, 1:30, 2:30, 3:30 & 4:30pm and Finding Nemo the Musical is showing at 10:00 & 11:30am, 1:45, 3:15 & 4:45pm.
I would advise you to see the very first Nemo showing as this show is extremely popular, that then gives you lots of opportunities to see Lion King later in the day.
I hope that helps and you have a great trip,
Jo