Hi can anyone give me names of

Unless you are looking for a specific recommendation,, try a search for "affitto casa lucca" think you will find most rental here is long term. Another would be to check out the forums (as you have with this) and give your requirements, many are living here part-time or in holiday homes and may well be happy to rent.

Thank you very much for the info - very helpful 

See>  http://www.viacarrara16lucca.it/

I know that Remax Viva, in the center of Lucca, handles long time rentals:http://www.remax.it/viva

Thank you very much for the info