Flame signal is Modbus 40014, scaled 0 - 100%
Hgps switch status: Modbus word 40036 or 40037 is listed as "Inputs". These are hard-wired inputs to the LMV3. Bit 11 is listed as "DW Max Gas" in the data sheet I have which dates back to 2004. If "Hgps" can be interpreted as "mercury pressure switch", a pressure switch set to turn on at some pressure measured in inches of mercury, that could be the high level switch while bit 10 labeled as "DW Min Gas" could be the low pressure switch.
Error Code and Alarm status: I see two data structures. One called "Lockout History" is 16 unsigned 16-bit registers. The first of those 16 registers is labeled "Error Code". The starting address is Modbus 400401. The rest of the registers are data related to that lockout. Then starting at Modbus 40417 is another structure for the previous lockout. There are structures for the eight most recent lockouts.
There is another 8-register data structure for "Error History" starting at modbus 40545. The first of the eight registers is the error code, the remaining seven are more data about the error.
Remember that you have to request the entire data structure. You can't request just the error code. You'll have to read all 16 or 8 addresses and sort them out in PLC logic.
You mentioned a burner control system. I was involved in a project about 20 years ago to control multiple LMVs using a PLC to bring them on or off line in sequence to maintain header pressure. As I recall, switching from keypad to Modbus control of each LMV turned out to be a bit tricky, but I can't remember the details.