Answering myself, and hope it will help someone.

On my testing environment, I fixed it this way:

-On the original server, script attach commands using T-SQL, this way (of course, use your own SQL path below):

SELECT 'CREATE DATABASE ['+ name +'] ON ( FILENAME = "'+ filename + '"),' + '( FILENAME = "F:\SQL_logs\' + name +'_Log.ldf") FOR ATTACH;'

FROM sys.sysdatabases

WHERE dbid > 4

ORDER BY name ASC

-Mount the LUNs via disk management

-Change MS-SQL data and log path to the new mount points

-Reboot SQL service

-Attach the databases using the previously generated T-SQL attach script.

After that, I was able to see my SQL databases and mount them via T-SQL.

Now, SQL2008 and above should apply required NTFS permissions on the target folders after changing the data and log path. If not, it can be forced and reset using this command:

icacls "E:\SQL_DATA\MSSQL\*" /q /c /t /reset

... then, attach the MS-SQL databases using the previous script.

where the path inside, is the actual parent folder for MS-SQL data or logs. The "*" cannot be omitted.

Once the NTFS permissions are properly defined, I