Note that "From now on" is quite a forceful expression. It is most often used with a rebuke or reprimand. A teenager has been brought back to his home by a policeman, for being intoxicated in town late at night. After the policeman leaves, the father reprimands him and says, "...and from now on, no going out of a weeknight, and on weekends, I want you home by 9p.m." The expression has the sense of someone being firm about some matter, 'laying down the law'.
From today on (I know I can say "From now on" but I don't know "from today on " is correct or not) we shall spend 8 periods dealing with/ learning/ studying/ discussing/ focusing on Lesson One.
For the next 8 lessons, we're going to be looking at Lesson One.
For the next 8 lessons, we're going to concentrate on Lesson One.
For the next 8 lessons, we're going to study Lesson One.
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