Thank you very, very much for all your feedback.
After reading more in depth, I have more informations and inevitable new questions.
At first, I am obliged to use LCDproc
since the software that sends information to display is set up for this.
I've seen some LCD2USB boards that, of course, are supported by LCDproc and should make everything easier, nevertheless I'd really like to find a (solderless) solution to exploit that unused pins on the VGA hat.
So, aside from LCD2USB boards, I wonder which connection board (I2C?) is OK to connect the LCD display to the pins of the VGA hat (I prefer a solderless solution so I'd like to buy display + connection board yet assembled).
Thank you again!