Contacting the Storage Admin may help (since you are using External Redundancy , Storage admin may help you -- using backup snapshot and stuff like that -- so storage admin may restore a snapshot lun and then help you on the recovery in the storage level -- raid integrity and rebuild if needed)
You may use RMAN -- as you may already guess. (Recreate diskgroup + DB restore)
You can create an Oracle Support SR, and consider using Oracle AMDU (ASM Metadata Dump), and extract the datafiles, and then register them and reuse them with a proper disk group. This may be an option.
You can create an Oracle Support SR , and consider using kfed to copy a header of good healthy to this failing disk, and then manually edit it in place to make it work.. (this is last resort, and requires lots of skills and low level knowledge)
So,
Storage Snapshot - first choice
RMAN Restore Up to last Archivelog - standard choice
AMDU Extraction -- If no backups exist
Manual kfed Edit -- only as a last resort
There are some notes , blog post that may give you insights on this.. For instance:
https://oraclehandson.wordpress.com/2010/08/06/cloning-oracle-asm-databases-with-kfed/