I'm not sure about that startup sequence, but let's solve this first. The Game Over relay is an interlock relay with two coils. The Latch coil fires at the start of a game and the Trip coil fires at the end of the game.
Jackpot Game Over latch relay (resized).jpg
There are three switches along the path in red that need to close for the Game Over relay Latch coil to fire. There are also other clues you can look for to narrow your search.

For example if your Total Play meter fires when you start a game you know that the Coin relay switch and Score Motor 1D switch are working. If your Ball Count Reset solenoid fires then all three switches are working and something else is preventing the Game Over relay from latching.

/Mark

Probably not. This part of the schematic is pretty different in Lady Luck. Your game over issue probably needs its own topic.