FULL WORKUP:
- We first convert the time to a string format in the desired output. using convert(nvarchar(50),time,121)
- We then substring out each time set so it can be summed together.
- Prior to summing we have to cast the string back to numeric value
- Now that we have the sum we have to ensure proper 0 leading padding right('00+convert...)
Resulting in:
.
Select 
  TotalWorkingDays, 
  sum(workingDays) as WorkingDays,
  Namer,  
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),12,2) as Numeric(2,0)))),2)+ ':'+
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),15,2) as Numeric(2,0)))),2)+ ':'+      
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),18,2) as Numeric(2,0)))),2)+ ':'+     
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),21,3) as Numeric(3,0)))),3) as LateIn,
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),12,2) as Numeric(2,0)))),2)+ ':'+
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),15,2) as Numeric(2,0)))),2)+ ':'+      
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),18,2) as Numeric(2,0)))),2)+ ':'+     
  right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),21,3) as Numeric(3,0)))),3) as LateOut 
from blue
Group by TotalWorkingDays, namer
using this example
http://sqlfiddle.com/#!3/81c0c/2/0
This has a significant issue however
Say a summed hour, minute or second exceeds 2 digits.  Your 53 is instead... 100... what should happen?  Presently this only looks at the two right most characters what should happen?
Your output can't be datetime datatype as 69 is not a valid minute... as in 10:69:00.000, thus the output;  So either the output is varchar, or your expected result is incorrect.
Now integration to your existing query:
With CTE as (
SELECT DISTINCT (DATEDIFF(DAY, '2014-06-01', '2014-06-30') + 1) - DATEDIFF(WEEK, '2014-06-01', '2014-06-30') * 2 - (CASE WHEN DATEPART(WEEKDAY, '2014-06-01') = 5 THEN 1 ELSE 0 END) - (CASE WHEN DATEPART(WEEKDAY, '2014-06-30') = 6 THEN 1 ELSE 0 END) AS TotalWorkingDays, COUNT(DISTINCT DATEADD(d, 0,DATEDIFF(d, 0, CHECKINOUT.CHECKTIME))) AS workingdays,
 USERINFO.NAME,
case when  '08:00:00.000' > cast(convert(char(8),min(checktime),8) as datetime) THEN NULL
ELSE 
cast(dateadd(minute,datediff(minute,'08:00:00.000',min(checktime)),'00:00')AS dateTIME) END as LATEIN ,
case when '17:00:00.000' < cast(convert(char(8),max(checktime),8) as datetime) THEN NULL 
ELSE
cast(dateadd(minute,datediff(minute,max(checktime),'17:00:00.000'),'00:00')AS dateTIME)END as LATEOUT     
FROM   USERINFO left JOIN CHECKINOUT ON CHECKINOUT.USERID = USERINFO.USERID 
left join departments on deptid = userinfo.DEFAULTDEPTID
WHERE(DEPARTMENTS.DEPTNAME = 'GEN/SUP-TBL') AND (CHECKINOUT.CHECKTIME >='2014-06-01') AND (CHECKINOUT.CHECKTIME <='2014-06-30') and name='Gokul Gopalakrishnan'
GROUP BY USERINFO.NAME,checktime)
  Select 
      TotalWorkingDays, 
      sum(workingDays) as WorkingDays,
      Namer,  
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),12,2) as Numeric(2,0)))),2)+ ':'+
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),15,2) as Numeric(2,0)))),2)+ ':'+      
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),18,2) as Numeric(2,0)))),2)+ ':'+     
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),21,3) as Numeric(3,0)))),3) as LateIn,
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),12,2) as Numeric(2,0)))),2)+ ':'+
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),15,2) as Numeric(2,0)))),2)+ ':'+      
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),18,2) as Numeric(2,0)))),2)+ ':'+     
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),21,3) as Numeric(3,0)))),3) as LateOut 
    from CTE
    Group by TotalWorkingDays, namer
OR the old fassion way...
 Select 
      TotalWorkingDays, 
      sum(workingDays) as WorkingDays,
      Namer,  
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),12,2) as Numeric(2,0)))),2)+ ':'+
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),15,2) as Numeric(2,0)))),2)+ ':'+      
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),18,2) as Numeric(2,0)))),2)+ ':'+     
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateIn,121),21,3) as Numeric(3,0)))),3) as LateIn,
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),12,2) as Numeric(2,0)))),2)+ ':'+
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),15,2) as Numeric(2,0)))),2)+ ':'+      
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),18,2) as Numeric(2,0)))),2)+ ':'+     
      right('00'+convert(varchar,sum(cast(substring(convert(nvarchar(50),LateOut,121),21,3) as Numeric(3,0)))),3) as LateOut 
    from (
    SELECT DISTINCT (DATEDIFF(DAY, '2014-06-01', '2014-06-30') + 1) - DATEDIFF(WEEK, '2014-06-01', '2014-06-30') * 2 - (CASE WHEN DATEPART(WEEKDAY, '2014-06-01') = 5 THEN 1 ELSE 0 END) - (CASE WHEN DATEPART(WEEKDAY, '2014-06-30') = 6 THEN 1 ELSE 0 END) AS TotalWorkingDays, COUNT(DISTINCT DATEADD(d, 0,DATEDIFF(d, 0, CHECKINOUT.CHECKTIME))) AS workingdays,
     USERINFO.NAME,
    case when  '08:00:00.000' > cast(convert(char(8),min(checktime),8) as datetime) THEN NULL
    ELSE 
    cast(dateadd(minute,datediff(minute,'08:00:00.000',min(checktime)),'00:00')AS dateTIME) END as LATEIN ,
    case when '17:00:00.000' < cast(convert(char(8),max(checktime),8) as datetime) THEN NULL 
    ELSE
    cast(dateadd(minute,datediff(minute,max(checktime),'17:00:00.000'),'00:00')AS dateTIME)END as LATEOUT     
    FROM   USERINFO left JOIN CHECKINOUT ON CHECKINOUT.USERID = USERINFO.USERID 
    left join departments on deptid = userinfo.DEFAULTDEPTID
    WHERE(DEPARTMENTS.DEPTNAME = 'GEN/SUP-TBL') AND (CHECKINOUT.CHECKTIME >='2014-06-01') AND (CHECKINOUT.CHECKTIME <='2014-06-30') and name='Gokul Gopalakrishnan'
    GROUP BY USERINFO.NAME,checktime) blue
    Group by TotalWorkingDays, namer