SQL Server 2017

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CREATE TABLE dbo.YourTable (LetterID char(1),
                            [Status] varchar(5),
                            DateTimeColumn date);
INSERT INTO dbo.YourTable (LetterID,
                           [Status],
                           DateTimeColumn)
VALUES ('a','info','20190201'),
       ('b','info','20190202'),
       ('c','info','20190203'),
       ('d','error','20190204'),
       ('e','info','20190205'),
       ('f','info','20190206');
6 rows affected

WITH CTE AS(
    SELECT LetterID,
           [Status],
           LAG(LetterID,2) OVER (ORDER BY DateTimeColumn) AS ID2Ago,
           LAG([Status],2) OVER (ORDER BY DateTimeColumn) AS Status2Ago,
           LAG(LetterID,1) OVER (ORDER BY DateTimeColumn) AS ID1Ago,
           LAG([Status],1) OVER (ORDER BY DateTimeColumn) AS Status1Ago,
           LEAD(LetterID,1) OVER (ORDER BY DateTimeColumn) AS ID1Next,
           LEAD([Status],1) OVER (ORDER BY DateTimeColumn) AS Status1Next,
           LEAD(LetterID,2) OVER (ORDER BY DateTimeColumn) AS ID2Next,
           LEAD([Status],2) OVER (ORDER BY DateTimeColumn) AS Status2Next
  FROM YourTable)
SELECT ID2Ago, Status2Ago,
       ID1Ago, Status1Ago,
       LetterID, [Status],
       ID1Next, Status1Next,
       ID2Next, Status2Next
FROM CTE
WHERE [Status] = 'Error';


ID2Ago
Status2Ago
ID1Ago
Status1Ago
LetterID
Status
ID1Next
Status1Next
ID2Next
Status2Next


b
info
c
info
d
error
e
info
f
info


WITH CTE AS
(
    SELECT
        LetterID,
        [Status],
        MAX(CASE WHEN [Status] = 'Error' THEN 1 ELSE 0 END)
            OVER(ORDER BY  DateTimeColumn ROWS BETWEEN 2 PRECEDING AND 2 FOLLOWING) AS Error_Flag
    FROM YourTable
)

SELECT
    LetterID,
    [Status]
FROM CTE
WHERE Error_Flag = 1;


LetterID
Status


b
info

c
info

d
error

e
info

f
info