Not sure what you are expecting but running the following all I see in the output is 1:00 PM to 2:00 PM which corresponds to the LunchStart and LunchEnd for the sample student:

DECLARE @t TABLE

(StudId INT, StartDate datetime, EndDate datetime,StartTime datetime, EndTime datetime, LunchStart datetime,LunchEnd datetime,flag bit);

INSERT INTO @t

SELECT 555,'2012-01-01 00:00:00', '2012-01-02 00:00:00','2012-01-03 07:00:00', '2012-01-03 16:00:00','2012-01-03 13:00:00','2012-01-03 14:00:00',0;

WITH Tally1 (n) AS (

SELECT TOP 100

15 * (ROW_NUMBER() OVER (ORDER BY (SELECT NULL)) - 1)

FROM

sys.all_columns

)

SELECT

StudId, LunchStart, LunchEnd,

dateadd(day, b.n-1, startdate) as effectivedate,

a.n,

b.n,

datediff(mi, LunchStart, LunchEnd)/15,

DATEDIFF(day, startdate,enddate) + 1,

Tstart = RIGHT(CONVERT(VARCHAR(100),dateadd(day, b.N-1, DATEADD(mi, (a.N-1)*15, LunchStart)), 0),7),

TsEnd = RIGHT(CONVERT(VARCHAR(100),dateadd(day, b.N-1, DATEADD(mi, a.N*15, LunchStart)), 0),7)

FROM @t

cross join Tally A

cross join Tally B

WHERE

a.N >= 1 and a.N <= datediff(mi, LunchStart, LunchEnd)/15 and

b.N >= 1 and b.N <= DATEDIFF(day, startdate,enddate) + 1

ORDER BY effectivedate ;

By the way, CTE's don't start with a semicolon (;). The semicolon is a statement TERMINATOR not a statement BEGININATOR and belongs on the statement immediately preceding the WITH of a CTE declaration.