Bert (and all),
the problem around I2C is more complicated as I have thought earlier. First, to understand both examples (working and non-wirking) above, it is necessary to study ByVac I2C LCD datasheet. The command $03 writes directly to LCDcontrollers, while command $20 recall routines of the MCU on he I2C ByVac LCD controller. There are of course more commands.

I did tests with all ByVac commands and changed step by step the "control" variable at I2CWRITE bit by bit. The "control" variable has no influence to I2CWRITE. Still I don't understand it's meaning.

The I2C analyzer shows bus conflicts / errors. On another place of this forums, in one thread, I have read user's problem with I2CWRITE in case of master/slave devices.

On the other hand, if I use assembler and write the communication from LAB-X1 to ByVac I2C interface to LCD in assembler, I can use without problems all ByVac interface's commands ... $03, $20, $25... etc., while PBP has problems.