Just to add one point -->

You were seeing path as "C:\Program Files\Microsoft SQL Server\MSSQL10_50.MSSQLSERVER\MSSQL\Backup\ C:\SQLLogs_LS\dbname.trn" .....

The path C:\Program Files\Microsoft SQL Server\MSSQL10_50.MSSQLSERVER\MSSQL\Backup\ would have been the default backup path for your instance... We did faced this issue last week and that is what I learned what a blank space can lead too.... Just thought to share ..:-)