Lilly had already seen the guy who had come to give the guitar. And there was no point in showing that video to her friend in london(I forgot the name) as her friend would obviously not recognise that guy.
Lilly wanted to show the video to her mother, as she thought that her mother must be knowing about it. So as soon as she landed in Berlin, she first decided to visit her mother.
And that why, maybe, she didnt tell her/force her/didnt know that Sunny could use gdrive. Instead of gdrive, she would have asked Sunny to send the video by mail too. But it didnt make sense to have the video in London.
You can find the following paragraph here in chapter 21
Lilly had almost forgotten it, but it made no sense to have it sent to London. Lilly wanted to watch it at home, when she would have the chance to visit her mother and ask her about it. She had replied that Sunny should keep the video safe until her return.