Riot, why did you nerf lichbane?

Reasoning behind this please?!

Early game it got better, mid game it got worse and late game it's now better (Than live)

Well...having an AP carry nuke you with physical damage was kind of dumb...

They buffed it significantly, and while also tweaking Deathcap on some champions you can actually do more damage getting Lichbane first over deathcap.
I don't wanna do all the math again, but I did it once and you can check it if you don't believe me. Going off their own respective items, assuming you are max level, a champion Like Diana using her whole kit would deal more damage with Deathcap. If she landed ONE proc'd auto attack, she does more damage with lichbane than she can do with deathcap. If she was to land 3, she would deal hundreds and hundreds more damage.

So depending on the champ now, items can be better or worse.

Relative to the other high tier items it is better now. Many major items like Deathcap have weaker stats and are now slightly cheaper as well. Thanks to the proc becoming magic damage, Lich Bane's changes were very good compared to how many other items were changed.

I don't understand could you possibly elaborate? Also just as a reference your ELO season 2?

It was nerfed because they didn't want ad champions building ap with dfg and lichbane, ad's that had abilities that applied on hit effects to now have 100% ap scaling that did physical damage example: Gangplank. Now it's really only viable on ap's that will need it like ap ezreal.

They buffed it really. So it only applied 75% of AP now, but that is because it does a flat 50 damage regardless of level, builds out of raw AP now and gives more of it instead of move speed and MR that were not really needed.
All this on top of making it significantly cheaper. It's more viable now, but if they had kept the scaling at 100% while making this changed, the item would have been on every mage, ever.

So, if I have 400ap and I proc lichbane I get 300ap + 50ap which gives me a net loss of 50ap. But the price was reduced because the MR was removed. Take out the 400g from nullmagic and you have the same lichbane with crappier stats. Also with the change to AP damage it makes enemy stacking MR easier. Soooo....

Is this incorrect?

Why are you complaining that your lich bane benefits from your magic penetration?
Let's use your example on a tank, Volibear. At level 18, Volibear has 96 armor and 83 MR getting the defensive masteries and armor yellows with scaling MR blues, pretty standard. This drops the 400 physical damage to 204 damage. Now, you probably have 8% penetration from the mastery, and the 9 Mpen red runes, so his effective MR is now (83*.92)-9=67 MR. This drops the magic damage down to 210 damage. This is without actually building any penetration items, no sorc boots, no haunting guise, no void staff, NOTHING. Unless they have high MR, low armor, and you have no additional pen, you're doing more damage.

Also keep in mind that each MR item now provides a maximum of 50 MR each(except abyssal, don't know if that's changed), versus randuin's/FH which give 70+ Armor.