100%

nothing changes onchain with ecash, lightning yes because opening and closing channels are onchain UTXO.

both ecash and lightning privacy will improve as the networks grow and high anonimity sets, but lightning is not a privacy enhancing tech whereas chaumian blind signatures yes.

All this to say, you have some privacy within an ecash mint, less privacy when doing ln payements to/from the mint, then even less privacy when opening/closing lightning channels onchain.