"Do not try to implement a scrolling window using LIMIT and OFFSET", then how?

I implemented a scrolling function for my sqlite table exactly against the rule #2 "Do not try to implement a scrolling window using LIMIT and OFFSET"

How then ? What I need is simple, return the previous X records or the next X records from the last time I selected.

Also, the article there said "This information is obsolete" but I just can't find the updated information!