You'll need a new SIM card, so going into the store to activate it would be ideal. Unless it's an older phone or has no SIM card. Then you can activate it online through your my verizon account under my account, my device, activate.
You don't always need a new SIM card, it depends on if it's retired or not or how long since it's last been used. I would try and activate it first, if not then follow MiiHere's lead.
If you read the post, he lost his iPhone = 99% chance that the SIM card was in it. There is that off chance that he is activating a phone that doesn't use a SIM card OR that he removed the SIM card before he lost it, but the SIM card is how he will connect to the network.
You are correct though, he can activate it online, but if it requires a SIM it won't actually be useful.
If he had a phone on his plan that was previously active before he purchased the iphone 6- and that if that previous phone had a SIM card in it-, then that's what I meant. Then he would be able to activate that one w/out needing a new Sim.