Hello David,
it is truly an impressive video. But it is a promo video, so I would imagine that not every single time it takes off so flawlessly and they used the "best" shots only. (here is the link btw
https://www.lily.camera/)
I don't think anybody tried it with Paparazzi, although it is possible. IMU/AHRS can initialize very quickly, and you don't necessarily need to initialize it levelled. One example would be external AHRS/INS devices, such as GX3 or Vectornav, which give you orientation quickly after startup (I assume they use gravity vector as a reference). Lily will have some cheaper solution, probably even the very same sensors as Lisa board. So the "only" missing part would be a better AHRS algorithm that doesn't need a long initialization.
I don't know about the GPS - maybe you can get some "fast" lock, although I doubt it. Maybe Lily flies without GPS just in altitude hold (barometer) until it gets a lock. The wrist control device is connected via bluetooth - so maybe some kind of RSSI is used to guide the copter while it waits for GPS lock.
Anyway, if the company delivers what they promise, it will be a cool product in a reasonable price range.
That's my 2 cents:)
M