If BA were going to sue Unite and sack strikers they would have allowed the last strike to go ahead. The timing was great as it would have had minimal impact on peak seasons and the strike was clearly "unprotected" so I think if this approach was going to happen then BA would have done it by now.
BA did not apply for an injunction following the last ballot, and thus it would seem would have "allowed" any strike to proceed. However they did write to Unite warning them that they considered the ballot to be flawed for several reasons, which in their view would make any strike unprotected. This letter would prepare the way for sackings and damages claims against the union.
As I've said before, I think Unite and individual CC are on very dangerous ground if they continue with further strike action. I also suspect that Unite know this.