I believe most character LCD modules have the metal frame connected to display ground, but possibly not all. Allowing ESD events hitting parts of an elecronic circuit without dedicated protection and some kind of error detection and recovery means inviting temporary failure and permanent damage.
In case of a display, there should be a transparent window with a breakdown voltage above expectable ESD voltage levels (e.g. 16 kV) and sufficient creepage distance around it's edges.
If the bus lines between the processor and the LCD controller have some length, ESD hitting the instrument case can still trigger false display characters in some cases. EMI standards allow at worst case temporary function loss of an instrumnet, but it most self-recover without user action. Refreshing the display periodically would fulfill this requirement.
I remember an instrument design where we implemented permanent background readback of the display RAM, calculating a checksum. Only in case of a changed display content the controller was reset and the display refreshed, almost unnoticed by the operator and without flickering in normal operation.