Is there any more information in the booklet? Because the box looks in good condition (apart from the top) and the coins at the bottom were from the 90s. Those at the top were from after the Second World War and should be made of aluminium, depending on year some are very rare, especially in almost perfect proof condition. The 500s and 1000 lira should be of silver. The 20 and 200 should be of aluminium bronze or brass, so should be brass colour.
So I am wondering if they are all mostly restrikes, as the brass ones aren't that brass colour, the silver ones haven’t toned and the aluminium ones are in perfect condition. This may have been something done before Italy started using the €uro, sold from the italian mint or national bank, you could try looking there as they may well still sell the sets.
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