There are several choices from YVR.

You could go back to LAX and then connect through LHR or DUB. The DUB connection means you will take EI across the pond. Having never flown EI, I am reluctant to recommend it. Also, I do not think there is a OW carrier flying the YVR-LAX route. Thus, you really can't do this with a OWE ticket.

A better option is to go YVR(AA)-DFW(AA)-LGW(BA)-EDI. You'll need to clear customs and go between the South and North terminals at LGW but it is much less of a hassle than going from T4 to T1 at LHR.

If you really want to go via DUB you can connect to EI at JFK but the flight times look like you will have to overnight at JFK.