Not that it'll be much help. I will say that menu systems can be a bit annoying (lotsa if then statements)
As far as your LCD dispaly, It might help to mention what kind you're gonna try. Theres several pretty easy ones Basic 20x4 Character LCD - Black on Green 5V - LCD-00256 - SparkFun Electronics Is quite easy to use. though you might have trouble putting your whole menu system on it.
For this you could probably do somethign like this
FIRING MENU
Rockets>>>
Ground>>>
as 1 screen, (the > before ground would be the indicator you move around to choose). Then say after picking ground. It clears the screen and does somethign like this.
Ground Menu
Ground Group 1
Ground Group 2
Ground Group 3
Then picking Group 1
Ground Group 1
Ready To Fire? (Displays, then when clickign yes the next line)
ARMED (holds here until fire is pressed, then shows next line for a couple seconds)
FIRE!! (Shows for a couple seconds, then brings back to the ground menu or something)
Oh yeha you said you have a mega, this will be very important, but never tell the thing to try and display !!!, theres somethign wrong with the 3! that causes a problem with the code, Hence why I only put 2 of them after FIRE
My worthless 2 cents though. I can give you a bit of a sample of a previous menu code that i had for a datalogger project before to show you my (albiet inefficient way) of navigating menu screens.