The sentence is saying the purpose of life is to be useful not happy. If a person is useful, honorable, and compassionate, than the person lives well and lives the purpose of life.
To live well is to make a difference with your life.
Here is a way to understand the unique wording:
[The purpose of life is] to have it (your life) make some (any amount of) difference that you have lived and lived well(with purpose, honor, and compassion). The phrasing implies living for your own happiness does not make a difference because that is not the purpose of life.
My dad's family is from the Chicago area, and my great-grandpa moved to the USA as an adolescent from Italy. The quote "to have it make some difference that you have lived and lived well" reminds me of Yiddish and Italian influence on American English in the 1900s which fits Leo Rosten's personal family background and his childhood in Chicago, Illinois, USA. I feel the words are a more humorous way to say "Make a difference with your life by being useful". Adding the word 'some' before difference implies living life to be happy does not make any difference at all, which nobody wants to happen! Everybody wants to make some difference ^.^