You mean you're trying to figure out what's going directly into the LCD, after the driver? Static LCD displays aren't complicated. They take AC power, so the power directly to the LCD is going to be swapped back and forth between power and ground, so if your logic analyzer can't take negative voltages don't bother. Even then, you don't need a logic analyzer for this. There's no 'logic' here. Except for the AC, it works like a LED display with a common ground.
Here's a basic tutorial on driving static LCD displays.
**broken link removed**