There's no real evidence that Lily was the favourite growing up, the only evidence we can use to support that is Mr and Mrs Evans' delight that their daughter is a witch. I don't think that conclusively supports the idea that Lily was the favourite because we only have Petunia's word and see so little of Lily's home life. In fact, given that the idea does come from Petunia, I would have thought, had there been clear favouritism, she might have made more out of it.
Lily is not at home for a fair amount of the year. That leaves plenty of time for Petunia to get undivided attention from her parents because she's the only child at home. When Lily comes home from the holidays, she would naturally get a lot of attention from her parents because she's been away for a while. Perhaps it made Petunia jealous, but I don't think that there was clear favouritism going on.
Wonderful avvie by psijupiter. Totally brilliant and amazing banner by Julia/the opaleye!