The only custom parts of a custom LCD are its size, and the transparent ITO electrodes on the glass. Typically, the electrodes are created with photolitography, which is somewhat similar to the process used for custom PCBs.
For LCDs, the setup costs are much higher than actual production costs, so you would not use them unless you planned to make a certain number of devices. The process is not as automated as for PCBs.
Dave Jones made several videos about a custom LCD for his USB power supply:
EEVblog #1055 - How to Design a Custom LCD
"How to design a custom multiplexed LCD display. Dave takes you through what is required to design your own custom LCD display and what consideration you need for manufacturing and choosing an LCD display driver."
EEVblog #1074 - Custom LCD Design - Part 2
"Looking at the manufacturers datasheet for approval, and test design considerations."
EEVblog #1105 - $100 Custom LCD Design - Part 3
"The $100 low cost custom LCD finally arrives! Will it work as intended?"
(Five modules for $138, including $33 shipping.)