As the error shows, you were trying to restore the database with a transaction log backup whose first LSN is 1587234000000358400001, however, the current database is just restored to LSN 1587227000001432600001. To restore transaction log backups, the log
chain must be continuous which means the last LSN of a previous transaction log backup must be the same as the first LSN of a transaction log backup that will be restored next. In your scenario, the LSN 1587227000001432600001 restored by the database full
backup, and the LSN 1587234000000358400001 of a transaction log backup is not the same, hence, the database restore failed because of the broken log chain.
If you were indeed restoring the correct transaction log backup, it seems be the reason that the current transaction log backup was ever overridden. For example, maybe you ran the backup log script twice by mistake and the backup log script with INIT option
enabled which means the existing file will be overwritten. In your issue, there is no way to restore the database with the current transaction log backup.
In addition, you can query the FirstLSN and LastLSN of each database full backup and transaction log backup and find that the LSN is not continual:
select name,first_lsn,last_lsn,checkpoint_lsn,* from msdb..backupset where database_name='SAMPLE_DB'
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