I don't know whether a replacement frame totally meets the sellers obligation under a "lifetime" warranty, or whether the warranty attaches to the replacement.

But the failue itself isn't all that rare. The BB shell/seat tube joint is possibly the most highly stressed joint on a frame, especially for strong riders, hill climbers, and sprinters. The high pedal loads alternating from side to side, create a rocking motion on the shell, which stresses the joints to the seat tube. Welded aluminum frames are especially prone to fatigue failures at the welds because of the nature of the welds themselves that create stress risers where the tube meets the welds.

As to you and Bianchi, I doubt you can win outright, but should be able to negotiate hard and get some decent compromise resolution that may be acceptable.