Here's a more concise way to do it. You can update the table by updating the CTE.;-)

WITH CTE AS(

SELECT *, ROW_NUMBER() OVER( PARTITION BY ID ORDER BY ltr) rn

FROM #tmp

)

UPDATE CTE SET

flag = 'Y'

WHERE rn = 1;

If your rank is not ordered alphabetically, you can simply change the column with the CASE statement in the ORDER BY clause