Another characteristic of a true apostle is he is not shy about declaring his apostleship. Paul did it. Peter did it. Paul plainly acknowledged the 12 Apostles.
"Then He appeared to James, then to all the apostles; and last of all, as to one untimely born, He appeared to me also. For I am the least of the apostles, and not fit to be called an apostle, because I persecuted the church of God." (1 Cor. 15:7-9)
Lee never boldly claimed he was an apostle. I was in a meeting once where he spoke. He told a story of a woman who approached him and asked, "Are you the apostle?" He said his response was to just laugh.
That wisdom seemed to have left him later on, as he saw the power advantage of people believing he had an apostle's commission. Even so, he still did not have the boldness to claim it. He just took advantage of the fact that some people believed it.
So, really, it seems silly to argue that Lee was an apostle if even he didn't claim it himself. If Lee wasn't bold enough to declare "I'm an apostle!" then why should we believe it?
Note also in the verses above that Paul again implies that a qualification for apostleship is "seeing Jesus." And also note that the argument could be made that Paul is implying he is the
last apostle.