The answer to this question is found in Chapters 1 and 2 of Maniac Magee.  In Chapter 2, we are told what the “Lost Year” is and in Chapter 1 we are told the basics of why it happens.

In Chapter 1, we are told that Jeffrey Lionel Magee (Maniac’s real name) was born and lived his first few years in Bridgeport, Pennsylvania.  But then, when he was three, his parents were killed in an accident.  He was sent to Western Pennsylvania to the town of Hollidaysburg to live with his Aunt Dot and Uncle Dan.  The problem was that they hated each other but would not divorce for religious reasons.  Jeffrey finally gets tired of their hatred for one another and runs away.

The Lost Year happens after he runs away.  He leaves Hollidaysburg and ends up in Two Mills (right next to Bridgeport) a year later.  It is only 200 miles and so it shouldn’t have taken that long.  As the narrator says

The question is: What took him so long?  And what did he do along the way.

The narrator goes on to say

The legend doesn’t have the answer.  That’s why this period is known as The Lost Year.

So, the Lost Year is the period in which the reader knows nothing of Maniac’s whereabouts or actions.  It is the year between when he leaves his old life and starts his new life in Two Mills.

What was the "Lost Year" in "Maniac Magee"?

Maniac is three years old when his parents die.  He lives with his aunt and an uncle that she lives with legally married, but he hates her and she hates him.  Maniac is very unhappy.  He hates their fighting.

'Maniac shouts out to them, above the voices of his classmates as they perform a school play, "Talk! Talk, will ya!" he is so upset that he begins to run, and Spinelli says, a legend is born. Readers hear no more until this strange boy shows up a year later in Two Mills, two hundred miles from Hollidaysbury. "

This year is the "Lost Year."