Well Vi has amnesia and it looks like VI was born in zaun.
it is possible that jinx went to piltover without knowing anything about VI,but then she recognized vi,because of VIs tatoo(she had that tatoo since she can remember).
I mean jinx seems oddly focused on VI,so it is possible that Jinx recognizes VI as her sister,but VI doesn't recognize jinx.
However you have a point about Lyte mentioning that Vi and her sister look similar,I mean jinx was pretty much designed to not look like vi.
But there are ways around that(maybe Vi has only a very old picture of her sister,I mean jinx could have changed a lot in terms of appearance(its been confirmed that her hair&eye-color aren't natural),or Vi could have a not-blood-related sister in piltover).
I still think the female mechanic that riot tried to get into the game(twice) is planned to be related to vi.(originally Vi was going to be a female mechanic,later on Braum was originally going to be a female mechanic,so Riot still wants to add that character).