So the secret is out: Renew foam is just renamed and reconfigured Lunarlon foam. Why rename a beloved and well-branded technology? Probably because someone realized that hyping React as a “Lunar killer” was not the most fore-thinking idea and there’s still a lot that Lunar/Lunarlon can do.
The Renew Run’s midsole is indeed Lunarlon (soft, nitrile-rubber-based foam encased in a slightly firmer Cushlon/EVA carrier) and feels closest to the Lunarglide 8. While that shoe was a very light stability model, the Renew Run appears to be neutral, as Nike continues to focus on all-consumer neutral models. The heel retains that plush cushion Lunar shoes are famous for, while the forefoot is a bit more responsive for picking up the pace.

The upper is incredibly barebones, practically being the same materials as Nike’s most entry-level running model, the Revolution 5. that said, it’s plenty breathable, just not as premium as the tail end of models under the Lunar banner (the Tempo 2, Glide 9, and Epic Low 2). It’s workable, functional, but won’t win any style points.
The Nike Renew Run actually has competition from its own company: The Zoom Winflo 6. That shoe features fore- and rearfoot Zoom units and is a little more performance-oriented. It is, arguably, also a better-looking shoe that can be found for cheaper. If you love that “walking on pillows” feeling, grab the Renew Run, but for everything else, pick up the Winflo 6.