On Evelynn I take QEW first three levels, then max R>E>W>Q. I don't build Liandry's unless health is stacked, and even then I might consider Blade of the Ruined King before Liandry's.
I think the 120% Attack Speed bonus from Level 5 E is better than 120 Damage from Level 5 Q. It really helps you stick, and by maxing W next you can get in and get out much easier. Q has such a short cooldown that you can keep spamming it without interrupting movement to apply the burn, since that's all you really need it for.
I'm still working on a set of runes and masteries that will make this Evelynn build the best though.