how to find out the log backups that I need to restore in order to bring log shipping from standby to online?
this script is to be run on server1 and gives me the latest log backup that is available

--------------------------------------------------------
--the latest backup for each database
--filtered by backup type
--------------------------------------------------------
declare @backup_type CHAR(1) = 'L' --'D' full, 'L' log

                ;with Radhe as (
                    SELECT  @@Servername as [Server_Name],
                    B.name as Database_Name, 
                    ISNULL(STR(ABS(DATEDIFF(day, GetDate(), MAX(Backup_finish_date)))), 'NEVER') as DaysSinceLastBackup,
                    ISNULL(Convert(char(11), MAX(backup_finish_date), 113)+ ' ' + CONVERT(VARCHAR(8),MAX(backup_finish_date),108), 'NEVER') as LastBackupDate
                    ,BackupSize_GB=CAST(COALESCE(MAX(A.BACKUP_SIZE),0)/1024.00/1024.00/1024.00 AS NUMERIC(18,2))
                    ,BackupSize_MB=CAST(COALESCE(MAX(A.BACKUP_SIZE),0)/1024.00/1024.00 AS NUMERIC(18,2))
                    ,media_set_id = MAX(A.media_set_id)
                    ,[AVG Backup Duration]= AVG(CAST(DATEDIFF(s, A.backup_start_date, A.backup_finish_date) AS int))
                    ,[Longest Backup Duration]= MAX(CAST(DATEDIFF(s, A.backup_start_date, A.backup_finish_date) AS int))
                    ,A.type
                    FROM sys.databases B 

                    LEFT OUTER JOIN msdb.dbo.backupset A 
                                 ON A.database_name = B.name 
                                AND A.is_copy_only = 0
                                AND (@backup_type IS NULL OR A.type = @backup_type  )

                    GROUP BY B.Name, A.type

                )

                 SELECT r.[Server_Name]
                       ,r.Database_Name
                       ,[Backup Type] = r.type 
                       ,r.DaysSinceLastBackup
                       ,r.LastBackupDate
                       ,r.BackupSize_GB
                       ,r.BackupSize_MB
                       ,F.physical_device_name
                       ,r.[AVG Backup Duration]
                       ,r.[Longest Backup Duration]

                   FROM Radhe r

                    LEFT OUTER JOIN msdb.dbo.backupmediafamily F
                                 ON R.media_set_id = F.media_set_id

                    ORDER BY r.Server_Name, r.Database_Name


and this script is to run on server2 and gives me the latest transaction log backup that has been restored:

-----------------------------------------------------------------
-- get the latest transaction log backup restored
-- modified from
--http://www.sqlservercentral.com/scripts/Backup/127480/
-----------------------------------------------------------------
SET NOCOUNT ON
SELECT
     rh.*,
    destination_database_name
    ,bmf.physical_device_name
    ,restore_date   
FROM        msdb.dbo.restorehistory rh
INNER JOIN  msdb.dbo.backupset          as bs   ON bs.backup_set_id = rh.backup_set_id
INNER JOIN  msdb.dbo.backupmediafamily  as bmf  ON bs.media_set_id  = bmf.media_set_id 
WHERE restore_history_id IN 
    (
    SELECT MAX(restore_history_id)
    FROM msdb.dbo.restorehistory
    WHERE restore_type = 'L' 
    AND destination_database_name IN 
        (
        SELECT DISTINCT destination_database_name 
        FROM msdb.dbo.restorehistory
        )
    GROUP BY destination_database_name 
    )
ORDER BY rh.restore_date DESC