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Join Date: Sep 2009
Location: Minneapolis: DL DM charter 2.3MM
Programs: A3*Gold, SPG Plat, HyattDiamond, MarriottPP, LHW exAccess, ICI, Raffles Amb, NW PE MM, TWA Gold MM
Posts: 102,617
The lounge showers I've used have all supplied towels (although perhaps not the number and size I would prefer or expect in a hotel) and minimal toiletries.
However, a few airports (IIRC in Asia) have public showers that might not supply towels.