There is some discussion as to whether or not the Prime Minister needs to be a sitting MP in order to be PM.

I am not a constitutional lawyer but will try to provide some commentary.  I would invite a constitutional lawyer to correct me.

The simple answer is "No, BUT..."

Canada is a constitutional monarchy.  The constitution is a combination of UK law, the 1867 BNA Act and the 1982 Constitution Act.  

This means that the head of state is King Charles represented through the Governor General.  The Prime Minister is the minister appointed by the monarch. The principle of responsible government is that the PM must have the confidence of the House of Commons.

The constitutional convention is that a PM must be either a sitting MP or about to become one.  If not, they must resign:The present status is that we have a PM (Trudeau) leading a minority government with the confidence of the House (NDP supporting).  He has prorogued the House until March 24, 2025.

The Liberal party will be undergoing a leadership contest at present with a leader to be determined by March 9, 2025.  Concerns have been raised as to lack of controls in regards to Liberal party membership raising significant risk of foreign interference.

A number of non-MP's have expressed interest in running for leadership of the Liberal party.  Let us assume one such individual wins the leadership contest: "Mary".

Having won the leadership competition, Mary does not automatically become the PM.  Rather, she must be appointed such by the GG.  

This creates a potential issue.  The GG could raise concern as to the process by which the Liberals elected their leader and decline to appoint Mary as PM given same.  If so, the GG would then either summon the House prior to March 24 or wait until the House resumed on March 24.  Trudeau would continue as PM.

That said, I very much doubt that the current GG would exercise her discretion against the Liberal party in this fashion.  Rather, I suspect that the GG would appoint Mary as PM but on the condition that Mary met the requirement of 'about to become a PM'.   That means that Mary must either shortly call a general election or seek election to the House through a byelection.  

Note: this scenario occurred with the leadership win by John Turner.   Once he was sworn in as PM, he requested that the GG dissolve the House for a general election:Thus, he satisfied the constitutional convention of 'about to be an MP'.

Concerns have been raised that Mary could attend the House on March 24, keep the confidence of the House with NDP support and then prorogue the House for many months, placing the election into the fall 2025.  I don't think Mary could do this as it would plainly breach the constitutional convention: she would not be 'about to be an MP'.  She certainly would not be following the precedent set by Mr. Turner of calling for a general election shortly after being sworn in.

There is one exception, however.  Mary could prorogue the House but only if an MP resigned, opened up a seat for a byelection and Mary then ran in that byelection.  This would satisfy the convention but I don't think this exception will occur. First, I doubt any current Liberal MP would give up their seat.  Second, there are no safe seats.  Third, typically, the Conservatives do not run against the Liberals (and vice versa) in such circumstances. However, I think the Conservatives would run heavily against Mary in a byelection (and likely win depending on the riding...).  

Thus, I suspect Mary would have no choice but to call for a general election.

Thus, I think the events now in question are leading inevitably to a general election in the spring 2025.  If not, then, in my view, there could well be a constitutional crisis...

Let me know your thoughts.