What is the lightest custom Android ROM (Android 4.0 or higher)?
There is no definite answer for this but here is my point of view - 
The Simple Solution - SlimRom:
SlimRoms - On-Click away,free, HTC compatible ROM.
With SlimRom you can configure how much of google services you wish to use which have significant effect on device performance. 
The Hard Solution - Create One:
You can create your custom Android OS and build clean version of it (without any google app like chrome or youtube).
If you really want to get wild you can delete all unnecessary apps under platform/packages/apps (e.g calculator,camera).
If you choose this option bear in mind that HTC specific features won't work.

More data:
If you're still not sure and need more data about specific features that you'll need in your app check the Custom ROM Comparison Database.