A few thoughts:
1. Have you tried setting the cursor before writing?
Private Sub AppStart
Serial1.Initialize(115200)
Log("AppStart")
lcd.Initialize(0x27, 16, 2)
lcd.Backlight = True
lcd.SetCursor(0,0)
lcd.Write ("Row 1")
lcd.SetCursor(0,1)
lcd.Write("Test")
End Sub
2. Have you tried changing the contrast poti on the i2c board? Even without a program running you should be able to see the block top left.
3. Try the address 0x3f instead of 0x27.
4. Check the address with an I2C scanner:
Link