The question has been "Why can't my Lone Scout be a member of the Order of the Arrow? Why can't Lone Scouts be a member of this "club"?
First, the Order of the Arrow is more than a "Scouting club". It is the BSA's national camping and outdoor programs honorary. It is supposed to be selective, and the way that members are nominated and elected makes it pretty unique among honoraries. The members elected to the Order of the Arrow (OA) are elected by NON MEMBERS of the OA...those in his or her Troop, Crew or Ship.
In order to become eligible for election, Scouts must have 15 days and nights, including a week of long-term camping, under the authority of the BSA. This means that family camping, camping done as a Cub Scout or WEBELOS Cub Scout, and camping with church or other community activity groups cannot be counted. This rule is in place because the OA depends on "honor campers", those boys and girls who have been camping with their peers and whose peers know them as "good campers". This also prevents the OA from becoming a "popularity contest" athough many Troops and Crews who camp a lot have figured out that the BEST campers to be honored in this way are also some of their friends whom they enjoy camping and hanging around with.
Remember, OA members don't elect new members -- youth members of the TROOP, CREW or SHIP do.
Second, the candidate has to be First Class rank or higher. This is non-negotiable. The Scout or Venturer must have the basic outdoor camping skills learned and earned as a First Class Scout, which includes nights and days camping which may be used toward being qualified for election.
Finally, the unit leader (Scoutmaster, Advisor, or Skipper) must approve all candidates before the unit conducts an election. This is to insure that the Scout or Venturer is deserving of the honor of being a member of the OA and to insure the youth is a registered member of a Troop, Crew or Ship.
Now where does Lone Scouting fit into this? Lone Scouts HAVE BEEN and MAY BE ELECTED to the Order of the Arrow but it's a hard trip to make.
The election is conducted by the local OA lodge during a meeting of the Troop, Crew or Ship. It's not done by mail, nor by teleconference. This is to insure that youth members are not being coerced into electing those who are NOT "honor campers and Scouts". I have attended Troop meetings as part of an Lodge election team to help those Scouts to elect those "honor campers" which best show values of service, brotherhood and cheerful service which are the three values of OA membership and participation.
The OA is known as the "brotherhood of cheerful service".
Many Lone Scouts get elected to the Order of the Arrow as a result of being a part of a Jamboree Troop or Crew. In that way, the youth of that Troop or Crew knows that Scout well, and can vote with a clear head as to his or her qualifications for election.
Some Lone Scouts spend a couple of weeks at their Council's summer camp program so that they could be a member of a provisional Troop, therefore getting the experience of being a part of a Troop and Patrol and therefore demonistrating their outdoor camping skills enough for the Troop to elect them during the summer camp period.
Again, please keep in mind that OA election does not equate to OA membership. In order to be a member of the OA, one must undergo a weekend Ordeal, which is held by the local OA Lodge typically at their summer camp or day camp facility and participate in the Ordeal ceremony. Again, this is an HONOR and not "something to earn" because one cannot "earn" OA membership.
For these reasons and explanations, the BSA's National Order of the Arrow Committee has denied Lone Scouts membership in the Order the Arrow. One must be a member of a Troop, Crew or Ship in order to demonstrate the ideals and principles of being a good Scout camper, of being of service to other campers, and good examples of the Scouting ideals including that of cheerfulness while performing tough camping tasks in an outdoor environment over a period of time.
As a Lone Scout, I could not be an OA member until I returned home and became a member of a Troop...and they elected me. I turned down the nomination the first time because I felt they did not know me well enough and because I was barely a First Class Scout. The following year, I did accept the Troop's nomination for election, and that summer I participated in my Ordeal at Camp Covered Bridge, located outside Louisville, Kentucky and became a member of the Order of the Arrow.
Hope this helps explain that there are some things, because of the way we do Lone Scouting, cannot be accomphished -- and why it cannot be accomplished as a Lone Scout.
(As a reminder, starting in 2019, female youth members may be elected by their peers in their Troop to the Order of the Arrow based on the same criteria male youth members are elected through. Some local Councils may allow girls to use their camping experiences as a WEBELOS Cub Scout count for the next two years toward OA eligibility...check with your Council for those specific details.)