I don't think there is a Lutheran equivalent to the Knights of Columbus, but there is no reason why you couldn't start your own fraternal group that does the same sort of work.
The KoC's principles are Charity, Unity, Fraternity, and Patriotism. It's most important focus is putting the love of God into practice and evangelization. It has a history of persecution from the KKK, Women's liberation groups (going back to the 1920s), and the Freemasons.
I've been to a couple of meetings and have really thought about joining, but one concern I have is that the main overseeing chapter has donated to a charity group that also worked toward promoting abortion. While it was an indirect act on their part, some Knights have left in order to not compromise their pro-life efforts. Despite the main chapter's donation, there are many, many great local chapters who have done an incredible job in spreading the message of Jesus through their sweat, their wallets, and their shoulders.