(not the op)

You absolutely could do the same without mixing first. Doing both adds a layer of protection in case you end up depositing your funds to a Lightning node that violates your privacy. None of these things are perfect you know. It's always possible that a privacy protection will fail. So layering them makes it less likely that all the layers fail at once. I think this is the reason why the OP suggested doing this via Tor and/or a VPN (https://www.ivpn.net/ accepts lightning!).

Also I think coinjoining the funds first is a good courtesy if your funds are potentially coming from sketchy sources. Like it or not "hot" coins are a potential issue. Coinjoining first means you aren't potentially giving someone a UTXO that could maybe cause them problems. They're kinda choosing to accept that possibility by accepting incoming transactions. But still, diffusion is good.

If I were running an LN node, I'd rather people give me coinjoined funds. I don't want to know where their money is coming from!