If you are using WoS or Phoenix but you don't know what they are using, yes, as a rule of thumb, you need to worry about them being online.

If they are using WoS or Phoenix, WoS can probably accept the payment offline and Phoenix runs in the background so it's usually okay.

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If he has a pubkey for the recipient, why does the recipient need to be online to receive the payment?

Because the recipient has to sign the new channel state

Ah interesting. Thanks for correcting me on this. 👍

Thank you. I really wish Lightning advocates would discuss this trade-off more clearly and openly.