When you check in for your UA flight and your connecting flight (I presume its UA for LAX-YYZ) you will need to provide your secure flight data to match a govt issued photo id (i.e. passport or military id) and that's the only data they need to match for you to fly.

Due to a software error my recent RTW ticket was issued with a middle name (where I have none) and the only thing that mattered was the name on the passport.

Get your UA locater number (even though you've ticketed LH there'd be a separate PNR from UA) and when you go online to ual.com it'd allow you to enter your secure flight information.