It would have to be an outsider candidate, and the LPC party structure does not do well with outsiders.

If you've ever experienced dealing with the LPC, you can see why: they're primary composed of compulsive board-of-directors members. Every Liberal representative and most of the party and riding executives are all from the same incestuous BoD members. They encounter each other all the time in their professional circles: they're on the committee for this, the board for that, the council for something else, the executive director for fill in the blank. They know each other because they're each other's lawyers, estate agents, consultants and so forth.

They're so socially inbred that it's incredibly difficult for an outsider to break in.

And before you say "All politicians are like this", they aren't:

• the NDP is getting this way, but they're not there yet; with the weakening of organized labour, more of them are from the Director class, but a lot are still union folk and a few are student radicals. They're nowhere near as institutionalized as the Liberals
• the Cons are composed of a mix of small-business douchebags and grifter-ideologues (sometimes in the same body!). It's actually pretty easy to break into the CPC: just have money and be a loud, obnoxious dick; support is something you can buy.
• the Greens are pretty much split between true-believers that don't like the NDP's professionalism, and grifters that are working a green angle for their next scam. Again, easy to break into if you're loud enough. (side note, it's scary how many failed Green candidates pivot to the Conservatives).

Compared to the above, the Liberals place a much, much higher value on consensus and favour-trading, and have a visceral reaction against outsiders.

By Liberal standards, Trudeau is an outsider candidate. What the LPC wanted was a Dionne or Ignatieff.