You could just have multiple clients attempt to update a row that defines the lock. Postgres transactions have no limit and will unwind on client failure. Since connections are persistent, there’s no need to play a game to determine the state of a client.
Your scenario still uses a centralised single postgres server. Failure of that server takes down the whole locking functionality. That's not what people usually mean by "distributed".
"the machines involved can fail" must also include the postgres machines.
To get that, you need to coordinate multiple postgres servers, e.g. using ... distributed locking. Postgres does not provide that out of the box -- neither multi-master setups, nor master-standby synchronous replication with automatic failover. Wrapper software that provides that, such as Stolon and Patroni, use distributed KV stores / lock managers such as etcd and Consul to provide it.
