Upvote:1
No, you can't, because no such airlines exist.
[Transport Canada] requires domestic air services operators [...] to be majority-owned and controlled by Canadians. [ref]
You could book a flight from Vancouver to LA on a US airline, of course. And might be able to book a flight to LA from Toronto via Vancouver through a US airline (through codesharing) but probably not with a long layover.
Upvote:4
You can buy the ticket from United, and it will be on "United Stock" (the e-ticket will start with their numbers, once upon a time it would literally have been printed on paper with their logo) even though it will be on "Air Canada metal" for the first and possibly second leg. It will be called something like United 4321 operated by Air Canada. This is how code sharing works.
Search for flights on United.com and you should see what you want. In a weird twist, such flights are often cheaper than buying from the operating carrier directly. I have no idea why.
Another trick, if you are ok buying your "free" travel with time, is to go through Chicago - YYZ-ORD-YVR-LAX. I'd buy my own ticket to YVR before I did that, but you might be able to work it out.
It's possible you can pull off the same trick with WestJet and Delta, but I'm not entirely sure. I have done a combined WestJet-one-leg, Delta-the-other fight all on WestJet stock, but I don't know if they have enough code sharing that Delta will sell you a WestJet flight. Also I bet YYZ-YVR has to change in Calgary on WestJet.