Lightning transactions can't be effectively traced to my knowledge. Funds make several jumps between network nodes, so an attacker would need to control at least every other node on the path to effectively track. Maybe a little less with some clever analysis.
Coin joins mix tons of inputs and outputs to make it near impossible to track whose coins are whose, but on-chain analysis may be able to trace things if enough participants in the join mess up and ruin their own privacy. Or, of course, if just you yourself mess up since it's all on chain.