ROME — In the lobby of the Bettoia Hotel Mediterraneo a second-century marble goddess now greets guests, blinking into the light after more than 30 years in a museum storeroom. We met Tracy Roberts, founder of Love Italy and the force behind Arte Fuori dal Museo. With around 85 percent of Italy’s state-owned art said to sit in storage, she wants hotels, and one day banks and post offices, to adopt forgotten works, fund their restoration and show them. The pilot already reaches about 10 Roman hotels.