Hi there, thanks for your feedback :)

Personally i feel that eve is really squishy so i like to build hp on her to stop her getting shredded in teamfights and when ganking and i like building warmogs as it will increase your bonus hp with cinderhulk.

The lich bane rabadons deathcap and ludens echo are only for the ap build route which i cover in the items chapter. I made the item build specific that if you are getting fed then you should buy ludens as it gains 20 stacks per ability cast and your q is up ever 1.35 seconds (with this guide) so you will reap great benefits and damage from it, please note that the a core item on the build is abysal scepter which reduces nearby enemy magic resist by 20 which will count towards her overall damage.

Please note that the jungle route is for the first jungle clear and evelynn gets very low on her first clear so it is unwise to do many camps in your first clear. I do this route as i personally feel that doing many camps then going b before you have enough money for the jungle item is a waste of time.

Hello, i'm also an Eve fan and im glad to see there are more! I saw you suggest few choices, which differ from my opinion and i wanted to drop a word. First, you put emphasis on HP, which i dont understand, as Eve has nothing to scale directly with HP. You say it will synergy with her ultimate, but its actually armor and resistance that will make the shield last longer. Ofc, its fine to pair Enchantment: Cinderhulk and Warmog's Armor, if you play as a fighter-off tank, since its in the current meta. Im also not convinced about Lich Bane, Rabadon's Deathcap and Luden's Tempest. They all become gold efficient only if you stack AP, which obviously you dont do going for high HP and no Archmage mastery. You will need quite high AP to make Lich Bane surpass other spellblade effects, in terms of additional damage. Luden's Tempest on other hand, will also need some magic penetration to make it worthy and Eve avoid such, since alot of her dmg is physical. Sure it will increase your sustain damage, as you said Hate Spike will proc it often.
Your jungle rout looks very scattered. You run back and forth between camps, which is a time waste overall, you can almost go back to base then return to the next camp while spending the same amount of time. Please take all this as a constructive feedback and ill be happy to see your thoughts.