Cycle Count

Thanks for posting an interesting problem
I created a small table like yours. I added a calculated column that added up the left and right columns. You'll see why when we get to the measure.

Since we need to access "the next row" and DAX has no built in concept of "next" or "previous" I also

added an index column in the query editor 

Now we need to write the measure that calcuates whether a given row should be counted as a cycle

Is Cycle =
VAR cur_index =
    SELECTEDVALUE ( Cycle[Index] )
VAR cur_both =
    SELECTEDVALUE ( Cycle[leftPlusRight] )
VAR next_row_is_one =
    CALCULATE (
        COUNTROWS ( cycle ),
        ALL ( Cycle ),
        Cycle[Index] = cur_index + 1,
        Cycle[leftPlusRight] > 0
    )
VAR count_as_cycle = cur_both = 0
    && next_row_is_one = 1
RETURN
    count_as_cycle

.We store the index value from the current filter context and the "left plus right" value as local variables.  Then we use CALCULATE to count the rows where the next row  has an index one greater (the next row) and a leftplusright is greater than zero (either 1 or 2)
then we return the combination of the next row being at least one and the current row being zero to say whether or not it should be counted as a cycle.

We can put this in a table graphic to check our results 

This code does not calculate whether the 1 in the "next" row is in the left or right column, it could be changed to do so.