The Lisa self test that occurs automatically when it is turned on or reset, displays the ROM version at the top-right of the screen. For example, if you see H/A8: H refers to CPU board ROM version 2.48 (48 is the ascii value of H, the 2 refers to Lisa 2.) The I/O board ROM version is A8.
For example: The 3A refers to the CPU ROM with a screen modification, the A8 is the I/O ROM version.
The I/O board ROM contains the instructions for the 6504 Floppy Disk Controller. Part of the static RAM used by the FDC is also used for storing preference settings while the computer is off. Otherwise, the I/O Board ROM is not involved with the many functions of the I/O Board.
Note that the version numbers may be misleading as various modifications exist, for example to allow the use of 800K floppies with MacWorks. (If you have details about these, please let us know so we can edit this answer.)
It is common for software to detect the type of hardware available by examining the I/O board ROM version
There are two flavors of these, one for normal Lisas and another for Lisas with the screen modification (always paired with the 3A CPU ROM.) The first version of the PROM is unique to each Lisa (aside from duplicated PROMs), because it contains that Lisa's serial number.
During installation, the Lisa's serial number is written to each copy of the Lisa Office System installation disks, as well as the tool installation disks (i.e. Write, List, Graph, Project, etc.) so they can only be used with the Lisa they were originally installed on.
Symptoms of serialized disks are that you cannot install the disks on another Lisa, and you cannot print if the serial # on the install OS does not match that of the one on your Lisa's CPU board. Instructions for deserializing the LOS floppies using FEdit are on the internet.
The screen modification kit PROMs do not have unique serial numbers. However, you cannot use the Lisa Office System with the screen modification kit. Only MacWorks Plus/II and the appropriate variant of MacWorks XL 3.0 will work with the screen modification kit installed.
The CPU board ROM is actually a pair of 2764 (8Kx8) EPROMs, which provide 8K x 16 bits for the CPU.
The I/O board ROM is a single 2732 (2Kx8) EPROM.
The video state machine PROM is a 256 x 8 bipolar PROM with tri-state outputs eg. MMI 6309-J.[LisaFAQ] > [Hardware] > [Lisa ROMs] (Comment on this answer)