That's very hard to do unfortunately, especially for a non-custodial platform like ours. There's too much fraud risk involved for us to offer that service.
However, we are looking to integrate other third-parties that do offer that exchange service.
For example, with Strike, your customer could pay you with USD from their Strike account and you would receive BTC in your Strike account. Granted that's a closed loop, but we believe more services will eventually offer fiat payments over lightning. When that becomes widespread, someone could pay fiat from Cash App for example, and it ends up as BTC your Strike account. That would be really cool! 

 Yes a third party. Something like this embedded on the invoice. 
https://stripe.com/newsroom/news/fiat-to-crypto-onramp 

 Yep. I think for us though it would be direct integrations with Strike, River, Swan, etc. that would auto-purchase as soon as funds have settled from a paid Zaprite Invoice.