No power to either of the 12 Volt auxiliary power sockets ("cigarette lighter" socket)
From looking at online parts diagrams I cannot figure out what fuse or relay might need to be replaced (or where it is located) but that is my suspicion as to why there is no power to either 12 volt socket
It sounds like you blew a fuse. No relays are used for aux sockets. If you have an owners manual it will be in there. The fuse box is under the back seat.
Actually a question is my fuse panel under my back seat in my 2008 Buick lacrosse cx 3.8 liter or was the info on your Table in picture
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