I can completely empathise with your feelings - my wife spoke to Lauren in the room at the Café Royale. Her group was also knocked out at this stage, and we've had the same comments from many people, asking why they were not put through to the live shows. I don't know, and I suspect that we never will.
My main point, though, is that this is not just a talent show - it is a TV show. The producers, and Simon Cowell, have to produce two hours of entertaining TV per week. Of course there were lots of talented people who deserved to get down to the top 40, and we can all argue that our friends and family were by far the best. But they have also got to provide a mix of different acts in the live shows, and this is not necessarily proportional to the people that entered the competition.
This means that the four live semi-finals will feature a number of dance troupes, magicians, contortionists, musicians and singers. Some will be kids, some will not - there has got to be a good spread. For Lauren, it could simply be the case that they decided to allow through five acts by kids aged 12 and below for the 'cute' factor, and she was number six on the list. Or equally, given that they tend to follow the background of the groups for the next stage in more detail, it could be that she has had her five minutes of fame on the audition shows, and they feel that there is not enough to add in the future stages to captivate the audience - we've all seen criticisms of this year's show for highlighting the sob stories. Realistically, a young lad who has been bullied and defies the bullies by pursuing his singing even after his nan and grandad died, his house burnt to the ground and his brother was sent to jail for a crime he didn't commit, is far more likely to get through than a middle class girl who has had every opportunity for fame through stage and theatre groups and supportive parents.
I'm not trying to be hard or disrespectful, but just see this show for what it is - TV entertainment, and if Lauren wants to make it big, BGT can just be part of the journey, not the end of the road.
One piece of advice I would give, though, is that Lauren's parents need to keep a tight rein on those around her - she may have actually blown her own chances by publicising her success through various websites and the press, when the producers had very clearly stated that no participants should talk to the media. Lauren appeared in her local paper on 16 January when she got through the first audition. If I were a PR officer on the show (and I am a PR consultant in the real world), I'd put a question mark over anyone who had broken this rule - the show works because the producers very strictly monitor what the media find out, so that they can release information to selected outlets as and when they choose in the best interests of the show. I should imagine that it will not have gone down well that her involvement in the show was being well-publicised before many of the acts had found out if they were through to the theatre shows. Whoever told the press actually broke a contractual term that Lauren's parents agreed to!
I do wish her well in her pursuit of fame and fortune - she is a talented girl - so don't see this as the end for her - she is young and has many years of opportunities, including next year's BGT if she so chooses...