Tony Fernandez & Team Lotus bought Caterham, but nothing to do with Group Lotus. The badge in the side of the Renault F1 is as a result of sponsorship by Group Lotus. The name dispute in F1 drove a wedge between Group L and Team L which is hard to fathom. Classic Team Lotus is something else entirely.
It's all a bit complicated. When Group Lotus discontinue the current Elise, it is speculated that Caterham may take over production.