In order to do what you want, all you need to do set the initial cursor position and then not set the cursor position between updates.
I guess that is essentially the same as "As long as you don't try to reset the cursor things should work as expected (until you fill up the screen).
Quiz: What do you expect to happen when you do fill up one line of the screen?
... and then you can scroll it to the left between each update.
I would expect that the use of lcd.autoscroll() would remove the need to do this, but then again things do not always work out the way you expect.
Don