One small caveat to keep in mind. At some airports, the lounge is in an international departure area that can't be accessed by inbound pax. Or by connecting domestic pax. Also, at CDG, the main AF arrivals lounge is outside security, so you have to go back through that process if you want a shower before your connecting flight.

Can't speak to LGW specifically. I do know that the DL "arrivals lounge" is in the Meridien hotel, and is just for BizElite pax, not STE+. No knowledge of the CO facility.