Although this sounds plausible, using a custodial client isn't really going to increase your privacy.
As per Moon's privacy policy, they keep logs on almost everything you do with their service.
More info here: muun.com/privacy_policy.html

If you want privacy, use a non-custodial Lightning wallet which doesn't rely on third-party to manage your channels.
It's a plus if you can connect your own node to it and can connect through tor.