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;'
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