In the past, I would have answered unlined. With the exception of the Speedo thong, which I unfortunately did not purchase before it was discontinued, most brands only offered unlined thong swimsuits.
These days, the thongs I wear most frequently are lined and have drawstrings. I like the classic swim brief–esque style, and the lining and drawstring help ensure I’m only revealing as much as intended. I still enjoy wearing unlined thongs and g-strings, but I don’t choose them as often.