"private" agreement between two c-lightning nodes on channel closure fee
Just use lightning-cli close id the implementation will first try to do a mutual close. Both lightning nodes will use the fee estimator from Bitcoind to suggest fees. If they don't agree there is a communication protocol defined in the BOLTs that they will eventually find a local agreement between themselves. This protocol is described under the section closing negotiation in BOLT 02 c.f.: https://github.com/lightningnetwork/lightning-rfc/blob/master/02-peer-protocol.md#closing-negotiation-closing_signed

Obviously both nodes need to be online and peered before you call the close command otherwise the node will do an expensive force close. Also it makes sense to wait until fees in the mempool are low if you can do that.