By reading Crypto-Note paper, I see that there is a diffie-helman key exchange.
To that end, does the receiver need to be online to complete that key-exchange?
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Yes, there is a key exchange, which implies two-way communication. But the first line of communication is the receiver providing their public address (public key, aka public spend-key plus public view-key). The information going the other direction is the transaction itself.
The transaction output is encrypted by the sender using the recipient's address and broadcasted to the network, where it is recorded by miners. When the receiver's wallet later scans the blockchain for outputs sent to it, the wallet's private view-key will decode the output on the blockchain, thus proving ownership of the output.
The receiver's wallet will only know it has a new output when it is online and scans the chain, so in that sense the answer to your question is yes. But the receiver does not need to be online contemporaneously with the sender because the blockchain keeps that record for whenever the receiver does get online.
Are you asking if the receiver of Monero coins need to be only in order to receive them from a sender?
If so then no. The receiver does not need to be online. The reason is that the transaction is stored on the blockchain. When the receiver goes online and his wallet syncs with the blockchain and if you send him some Monero before, he will see these coins in his wallet. No matter when he goes online.