There's an official port of MIUIv5 for our P780 which can be found here.
It needs the Chinese base and not the International one, which means you need to have a Chinese stock ROM before flashing MIUI (flashing over the international stock rom ended in a bootloop for me).
I installed it a week ago and so far it's working flawlessly with a minor issue with the CSipSimple application (opening the Settings dialog causes FC). Didn't find any other bugs, running smooth on the P780 4GB version.
***BEFORE YOU CONTINUE***
Please note, I'm just sharing my own experience with the community, hoping this would be useful to someone.
I don't take any responsibility for any damage to your devices should you decide to follow the steps below!
What you do with the content of this thread is your own responsibility.
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What I've done to run MIUI on the Lenovo P780 (4GB):
Since my phone came pre-rooted I didn't have to do it on my own. There's a good guide for rooting here. VibeROM can't be rooted via framaroot, so you'll have to find another way if you're running it and don't have root.
Download Mobileuncle Tools and backup your IMEI. I suggest keeping it somewhere safe in case of trouble.
Download MtK Droid Tools and backup your whole current ROM (takes a while) so you can flash it back with SmartPhone Flashtool later on if you decide.
II. Flash Chinese stock ROM
Download the Chinese S135 base stock rom along with the drivers and the flash tool from here and flash the S135 following the instructions provided.
Let the phone boot at least once. Copy the MIUI zip on the phone.
III. Flash MIUI
Reboot into recovery (shutdown the phone, then hold Power + Volume UP + Volume DOWN until you see the TEAMWIN logo). Perform a factory reset (Wipe Data + Cache) and Wipe Dalvik Cache.
Select Install and choose the MIUI zip archive, wait for it to flash.
Reboot phone and enjoy MIUI
IV. Some screenshots:
You can see them here.
Finally, I'd like to thank the authors of the threads and articles linked in this post.