only that they lead the party

That is convention, but is not a requirement. Canada's political system makes no special consideration for parties. It is entirely based on individuals. Freedom of association allows for individuals to belong to a party, of course, but that membership is only relevant to the worker who belong to it.

After all, political parties are just the labour unions of the political workers. It really wouldn't make any sense to involve union membership as a requirement in the hiring process. From the employer point of view, who cares what union a worker belongs to? It matters to the worker, but nobody else. If it were any other organization, you wouldn't think "Oh, this applicant must be better because he is a member of Unifor and not UAW." You are going to look at the qualities of the individual and what they can do for you as your employee. Government is no different.

But it stands to reason that the workers of a given union will prefer to see their union boss as Prime Minister as they already have a special relationship, so if a given union has control of the House they are going to push for that boss to be PM. Hence the convention that has been established.