How to implement a LN referral program

Dear bitcoiners,

I would like to implement a referral program for my ecommerce.

For example, if someone accesses the site via referral and complete a purchase within 24 hours, a percentage in BTC is automatically sent to the ref address indicated on the URL.

This is a pretty easy task to do with "regular" addresses, but is it possible to do this via LN, avoiding on-chain TXs?

It seems to me that the only existing way to bypass the creation of the invoice would be lnurl, but it is apparently quite experimental, poorly supported and complicated to automate via API without using exotic services.

Any experience or advice on this?