I believe SQL Server will no longer be available - or, at least it will have problems.
Not that I have had multiple files on separate LUNs where I lost one file, but I have lost the LUN for tempdb and SQL Server will crash. Once the LUN is available, the you can restart SQL Server and it will come back up.
Note, if you lose a LUN for just a few seconds - that is enough to cause SQL Server to fail. And once it fails, the only recourse is to restart.
Jeffrey Williams
“We are all faced with a series of great opportunities brilliantly disguised as impossible situations.”
― Charles R. Swindoll
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Managing Transaction Logs