First off, I can completely empathize with how disappointing it can feel to be rejected from a firm you really like and after putting a lot of effort in the application. However, remember that this is no indication as to your worth - even the very best candidates have to face so many more rejections than acceptances. The cycle before last I was rejected at first stage in every single application. The way I eventually turned the situation around was by refusing to give up, always coming back more committed to doing better and to keep moving forward. I think this is the only way to succeed and this is the attitude I would advise you to try to embrace.
Secondly, it is not that uncommon for people to be rejected in one competitive application and be accepted in another in the same application cycle and at the same firm - I remember
@Ram Sabaratnam wrote about being rejected for an open day at
Cooley and still getting a VS and TC offer afterwards. Since applications are so competitive, progression is a game of small margins as recruiters have to make judgement calls in deciding between multiple strong candidates. I think a combinations of potential improvements in your application (even if you think your Lift Off applications were really good, trust me that there is always room for improvement) and the factor of luck (as different recruiters on different days will emphasize different criteria when making those difficult judgement calls) could definitely lead to VS progression, so I think it is worth a shot.