Amboss doesn't know about your lightning transactions; they only run the channel marketplace, but whichever swap service you use would know about your transactions.

(not OP)

If you're doing that aren't you giving information on your txs to Amboss? I don't trust them. They're into AML/KYC bullshit.

anon

This completely breaks the relationship between your previous UTXOs and your new UTXOs.

bitcoin

How I spend my coins privately with Coinjoin and Lightning

There's a way simpler way to do this.

1. Have lightning node
2. Buy channels from Magma
3. Loop in 

This completely breaks the relationship between your previous UTXOs and your new UTXOs.