First of all where is Lerici? It is located in the region of Liguria (one of Italy’s smallest) on the Mediterranean cost between Genova and Pisa. Two nearby towns have train service, Sarzana and La Spezia, which is the larger and is a major departure point for Cinque Terre.
Airlines with direct service:
United Delta American Alitalia Emirates
IAD to FCO JFK to FCO JFK to MXP JFK to FCO JFK to MXP
EWR to VCE JFK to MXP ORD to FCO JFK to MXP
EWR to MXP JFK to PSA* MIA to MXP ORD to FCO
EWR to FCO ATL to FCO MIA to FCO
ORD to FCO ATL to MXP BOS to FCO
DTW to FCO LAX to FCO
Direct service is not the best alternative (in my opinion), with the exception of summer service that Delta offers to Pisa*. Rome is too far away to be convenient. Milan is not too far if you are renting a car, but it is still an hour by train just to the main station in Milan.
Pisa and Genova are my favorite choices if you have a good connection through Paris, Frankfurt, Munich, London or other European gateways.
I have connected into Turin, Genova, Bologna, Florence, Milan, and Pisa.
Pisa is less than an hour by train, Genova about an hour+, the rest are about 2-3 hours to Genova and then change to La Spezia (Malpensa adds an hour to get to the main station in Milan).