The short answer is this: The parties can certainly draw up their own agreement, but it’s always best to have a lawyer review it, nonetheless.
Technically, a Cohabitation Agreement or other Domestic Contract (including a Marriage Contract or Separation Agreement) does not have to be prepared by a lawyer. As long as the parties to the agreement are on-side with all the terms, they are free to prepare it themselves.
However, there is a great deal of risk associated with this. Despite the parties’ best intentions, it may not cover all the legal issues they intended to address, may be worded imprecisely, or may be based on misunderstandings around how Canadian Family Law works. Without the guidance of a lawyer, the agreement may end up breeding confusion – or worse – a dispute, necessitating a trip to the courthouse to have it resolved. (Plus, a lawyer can ensure that, once satisfactorily drafted, the agreement is validity signed and witnessed, in accord with legislation governing formal validity requirements.)
So even if both parties are on-board to prepare the agreement themselves, it is always best that they have it reviewed by a lawyer – or more precisely, by two independent lawyers (i.e. one for each of them).