Extremely low range on abilities.
That's what her W is for, much like Lee sins Gap closers. There is also always flash and ghost as well. I'll agree that overall, Lee has much greater mobility
Horribly low defensive stats.
Lee sin has Stats in general compared to Eve, with the only stats better being starting HP and AD Base from 1-18, with MR being the standard 32-53 for both. We can argue about the MS, but Eve does also have a good gap closer, and granted she generally builds
, she has some great movement and stickyness added on as well.
Horribly low base damage.
She is an assassin so her scaling make up for that. Her Q is also on a very low cooldown, so while 1 Lee Q does (340) + (180% BonusAD) + (8% missingHP) every 7 seconds (no CDR), Evelynn can do ~(240 + (280% bonusAD) + (220% AP)) in the same amount of time. her scalings are much better than Lee's in general.
MANA COSTS
Certainly nowhere near as strong as Energy, she does however have good regen when her passive kicks in. This allows her to wait for a prime opportunity to gank. A good Eve player, such as you, will probably wait a short time before engaging to ensure you have mana available. Lee can gank whenever.
These are what i specifically disagree on, however, the worst offender:
...and on top of this he [Lee Sin] scales harder than Evelynn .... remember that Lee is brainless easy to play as well.
Alright, I'll tackle that first one. He does not scale better than her. He scales until about 15 minutes in, then, falls all the way down, never to rise again. The longer the game goes on, the worse he becomes. Without any sort of lead, even going even, Lee is behind. In the first 15 minutes, his winrate is between 53-~55. 5 minutes later at 20, he has a 52% winrate, then at 25, 49%. It keeps going from there, all the way to below 45% at 50 minutes. This winrate is consistent with all tiers, with minor deviations on where the high is (I picked the highest which is in gold+), and when he is lowest. There is also a strange deviation in Diamond+ of him having a 60% winrate at 50, but I'm fairly confident that the Lee's team won the game rather than himself, but also doesn't represent Lee's late game and is negligible.
Evelynn goes up and down like a roller coaster. Her winrate is also fairly incosistent among tiers, but has a similar path of highs and lows, probably denoting item spikes. In plat+, she has 3 high points and a sharp low. At 10 with ~54%, 25 with 48%, 40 with 52%, and finally ending with a 51% at 50. Diamond+, again, shows some devations from the norm, with a very strong 63% winrate at 10, and doesn't dip to below 50% until after 40, where it spikes again to 60% at 50.
Again, diamond+ isn't a good representation, but its still interesting to see how the top players do.
In terms of difficulty, the win curve also shows it quite well. Lee is more difficult on average, what with landing a skillshot (which gets ever so slightly harder as the game goes on with the increase in mobility), ward hopping with good timing, and actually choosing a good time to try for a pick (his damage clearly falls off and cant always finish off his foe later on.)
Lee Sin is not Caitlyn, he is an early game bully that falls off, so to ask for his late game to be gutted is harsh and should not be something we ask for of any champ. If any nerfs were done, I would like for Riot to explorer reducing or removing his Q execute. Baby steps.