How can I encode an MP3 file in Android using LAME? Can anyone tell me how to encode a MP3 file in Android (as you would by using lame.dll in Windows or lame.so in Linux)?
You can't use the Linux or Windows versions of LAME in Android, just like you can't run the PC versions of MS Word or OpenOffice in Android.  Applications are written for particular OSes and architectures, or for cross-platform frameworks like Java.  (Android doesn't have a true full JVM, though.)

A quick search returned Lame4Android, an Android app you can use to encode WAVE files as MP3.  It doesn't look like it can do anything else; if you need more functionality then you probably need to find or make a native port of LAME or another encoder.