As this question and 'Linear Programming in Android' in general is a rarely discussed topic, I figured I would post my findings here for anyone searching in the future.
BTW, I ended up using a port of Ojalgo, given below.
These are the LP Libs that I found can be readily imported into an android project :
Perhaps the most well maintained library, this one supports Linear Optimization but does not have "Integer" LP.
The next two libraries do support Integer LP and/or Mixed Integer LP.
Even though the Latest version of Choco (4.0) is based on Java 8, there is a Java 7 variant of version 3.3.3 . You can find it here. This imports into Android Studio without any issues.
Another issue you might run into is that even though there are guides and tutorials on their website for version 4, you wont be able to find any guides for Choco 3 except for the Javadocs. But fortunately someone had made a PDF of the older guides which you can get by Googling "Choco3 User Manual".
Also note that Choco is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. So if you want to use LP in a commercial project, consider the next option.
Ojalgo is another great library which has an MIT Licence and supports Java 7. But as I found out, it uses a couple of Java calls that is not available in Android.
Luckily, an MVP has ported the library to work in Android : KIC/ojAlgoAndroid
This port ran with no issues. I have forked and created a release on Jitpack : shahimclt/ojAlgoAndroid.