These Lie groups had been the focus of earlier research of mine with Sonia Stanciu. In fact, Sonia and I had observed that the plane-wave limit of the AdS3 x S3 background of (1,0) six-dimensional supergravity could be interpreted as a group contraction, a result which was contained in Sonia's last paper Penrose limits of Lie branes and a Nappi-Witten braneworld, which appeared posthumously.
Lorentzian Lie groups also play a role in the classification of parallelisable backgrounds of ten-dimensional type II supergravity. A classification of the non-dilatonic backgrounds can be found in On parallelisable NS-NS backgrounds. Teruhiko Kawano and Satoshi Yamaguchi took care of the dilaton and, together, we later determined the Parallelisable heterotic backgrounds.
My latest (and, at least for now, possibly last) project classifying supergravity backgrounds concerns the Freund-Rubin backgrounds; that is, backgrounds where the fluxes are dictated by the metric. This work, done in collaboration with Felipe Leitner and Joan Simón, is being written at the moment. It borrows heavily from Felipe's work on lorentzian manifolds admitting twistor spinors and from previous work of mine with Bobby Acharya, Chris Hull and Bill Spence on Branes at conical singularities and holography.