The problem with this sentence is that the participle “nicknamed “Lucky”” is awkwardly placed. There are two ways to solve this problem.
A participle is a phrase that goes along with a noun that explains the noun. In this case, the noun is Charles, and the participle is “nicknamed “Luck””. It is a participle because it is a verb (to nickname) made into an adjective, or descriptive word. In this case “nicknamed” describes Charles.
If you put the nickname in parenthesis, you set it off and make the sentence flow better.
At a museum we saw a life-size replica of the Spirit of St. Louis, Charles (nicknamed "Lucky") Lindbergh's famous airplane.
The problem with this arrangement is that it is still awkward. An alternative is to get rid of the participle phrase and use an appositive instead. An appositive is a noun that describes a noun. Usually when we refer to nicknames, we do this.
At a museum we saw a life-size replica of the Spirit of St. Louis, Charles "Lucky" Lindbergh's famous airplane.
This sentence is clearer and less awkward. It still contains the same meaning because most people realize that the word in quotation marks is a nickname.
Please note that I also added a space between the period in St. and the word Louis.