This is not a proposal of forking network!
Yes, it is.
A coin is forked after blocks are generated with both the new rules and the old rules. You are proposing new rules to return "lost" bitcoins somewhere (back to the sender?) The old rules say that a transaction must include a valid signature of the address holding the coins, but your new rules would not have this signature (because the private key was lost). Therefore blocks created with your new rules would not be valid under the old rules.