What is a Lira in the US worth?

Actually, nothing nowadays. Italy switched to the euro back in 2002 and lira were taken out of circulation.

There are a few major banks and other agencies that will redeem obsolete currency but unless you have a large quantity of lira it's probably not worth it. Back in 2002 the lira was worth about 1/10 of a cent so you'd need quite a lot to make it worthwhile.