How are dot matrix LCDs controlled?
Microcontrollers that drive LCDs are typically for driving segmented LCD with very few segments. They are typically made of custom LCD glass and how the display is multiplexed is built into the LCD glass itself. You will need to check with the display vendor to determine how many common and segment lines there are for your LCD and how they are wired. For a dot matrix LCD you will probably need an external LCD controller. The LCD display vendor can probably recommend one.

For some background in how a on-chip LCD module works.
Microchip application note AN658

EDIT: NXP Has a number of LCD segment drivers available and application notes explaining how to use them. I have not seen a microcontroller that has a built in LCD driver for more than a few segments and certainly not 1024. I'd recommend something like the PCF8576C. You can cascade multiple chips together to drive more segments.