A custodial lightning wallet doesn't eliminate the kyc trackability, it merely transfers that trackability (from the original exchange to the Lightning custodian). If you don't trust the original exchange with your privacy, but you do trust the Lightning custodian, then this is sufficient.

If you don't want to trust ANYONE with your data then you should coinjoin your on chain funds with Wasabi Wallet or BTCPay Server's coinjoin plugin (and then open Lightning channels with your coinjoined funds if you choose to add another layer of privacy).