You snuck that last one in just as I was about to say thanks for the update.
I was going to do as we discussed by PM and add to this thread -- but kind of at that very moment I got sidetracked by seeing that the results were in on the very first two DNA tests I had ordered for the two sides of my family and I got all excited and have been playing with them ever since! (Fortunately, it was a long holiday weekend here in Canada.)
I would suspect that she really was the daughter of Susan and Samuel - it's a bit of a pain that both Susan/Susannahs went by both versions of the name at different times.
But on her baptism, the mother wasn't referred to as a singlewoman, and the father's occupation was given. The baptism was in August 1891, and Samuel Rush and Susan Smith had married in the June quarter of 1891, and the birth was registered in June quarter 1891. Much more likely this was the couple.
Of course, the actual birth certificate for Elizabeth Ann Rush would tell you who her parents were -- I would definitely get that certificate so you can be sure, because otherwise if you want to go farther back you can't be sure you're on the right track.
The Cornwall OPC who transcribed the baptism is a member here. I'll PM you her contact info at this site. She might be able to tell you whether the baptism record actually makes it clearer what mother Susan's status was.
Unfortunately, I think we have to conclude that Lily didn't actually marry George Henry Evans, perhaps because she was underage when their relationship began, so there is no marriage certificate there to show her father's name.
Very glad to have helped!