That'd be the same Lightning Network with NP-hard issues with routing and a whole host of problems right down to the fundamentals, right? (1, 2, 3, 4, 5, 6)
And even beyond that, having to stack another layer on there is a technical non-starter to begin with. For one thing, adoption of the Lightning Network is fundamentally bottlenecked by Bitcoin itself - if the entire Bitcoin network was dedicated entirely to onboarding people onto the Lightning Network, it'd take 28 months to onboard all of the people in the US alone, let alone the rest of the world's population.
There's a saying by Antoine de Saint-Éxupery that's rather relevant here: « Il semble que la perfection soit atteinte non quand il n'y a plus rien à ajouter, mais quand il n'y a plus rien à retrancher. » Roughly paraphrased, it means, "It appears that perfection is attained not when there is nothing left to add, but nothing left to take away." Trying to stack extra layers on top of a precarious base goes against any sound engineering principles. In this circumstance, Bitcoin would be the thing to take away - it offers nothing and is in fact detrimental to an efficient system of exchange.