Why is message D required?

[jprupp]

Message D means that the anchor transaction was confirmed in the bitcoin blockchain. Watching the blockchain directly is enough to know when this happens. It is not necessary to exchange further messages.

[matsjj]

I would stick to it for now, as it eliminates some risks of incoherence between the parties. While both parties know how many confirmations the other party wants the anchor to have to consider it safe, we don't know which view the other party has of the blockchain. Maybe it is on some part of fragmented network and only sees the block 1 minute later?

Either way, LNEstablishDMessage is just a signal to say that one is ready to accept / relay payments now.