From both perspectives, Allen joining the Lib Dems is a no-brainer. South Cambridgeshire is the sort of Remain-facing Tory seat that the Lib Dems should be targeting next election, having the incumbent join could boost their chances by bringing over some of her personal vote, while Allen would probably have a stronger chance of winning with a party label.
'All [people] want is someone to love, somewhere to live, somewhere to work, and something to hope for.'
If I remember correctly, Allen has made comments in the past couple of weeks which hinted towards her not wanting to join the Lib Dems. I do not believe for one minute that the central party would have turned her down; however, I have heard that the local party in her constituency, whilst positive of her, don't want her to automatically be their PPC. Maybe that put her off; although I hope not.