Given the intended purpose of that "l.p." app, it is not obvious that anyone on XDA should help you - potentially that is the same thing as assisting someone who is trying to defraud a software developer.
Having said that though, I'll assume that you are merely a researcher.
1) You can repackage the app by only modifying it's Android manifest to remove networking privileges, and repackage it by signing with your own key. (A researcher would never redistribute such an .apk however, as that would not only be fraud, but theft as well).
2) The above alone will likely cause a failure in the application's code - possibly even a FC. Even if it does not cause a complete app failure, there is nothing that prevents an app's internal state & control from being contingent on results from network communication. So (for instance) the only away around something like
Code:
if ( network_checks_pass() ) { good_stuff(); }
(assuming a soft-fault in network_checks_pass(), rather than a FC)
would be to reverse the code, modify it, and recompile it (in addition to the privilege changes in the manifest). For that you probably want small/baksmali and some coding skills.
Again, to be perfectly clear: a researcher would never redistribute such an .apk however, as that would not only be fraud, but theft as well. Using a paid app for it's intended purpose without compensating the developer is fraud, plain and simple.
About the only time such behaviors are acceptable is if you modify an app
that you have already paid for - and then you keep it for only your private use.
good luck
.