When you move your sats to fund onchain lightning node here you already gave up your privacy unless you opened onchain lightning opening using postmix tools. So that’s #1 step that is most important because some entity knows that this utxo that belongs to you was used to open that LN channel. 
Also muun is not a lightning wallet it’s actually an onchain wallet with an onchain to lightning swap service. It’s not a true LN wallet, even when you receive LN onchain fees are paid. Also muun charges a fee for failed payment attempts and they simply approximate by paying you LN with a swap onchain balance into LN and they pay an invoice for you. 
Also using this tool https://lightningdecoder.com/
Your LN tx are not private 

 I think lightning tx are private if I do not have a direct channel between payer and receiver. Lightningdecoder.com does not discover any identifyable information.