This is the screen capture of the logic analyzer software (zeroplus) used to illustrate i2c communication between an Arduino board and the serial LCD module. As indicated in another post, to use i2c, you need to solder a jumper in R1.

The light blue tag is i2c START
0x28 is the address of the serial LCD module
The next tag is WRITE (dark orange)
Next is the A-ACK (address ACK)
Then you can identify several data like 0xFE (escape character to send commands to the LCD controller), 0x45 is the cursor position command ID, 0x44 is the cursor position data (2nd line, 5th character), 0x03 is the character (I am running the CustomCharacter example, where character 3 is the little man with the hands down), then finally the STOP tag
After each DATA, you can identify the light green tag which is D-ACK (data ACK).
Hope this helps visualize what is being transmitted through the wires in i2c mode