Is it possible to write a platform independent application in Java ME & LWUIT?
More specifically, can I write apps which run on both Android and Blackberry?
Answer is NO. LWUIT is great for J2ME development as it enables SWING kind of development approach in J2ME but for Android and BlackBerry LWUIT is not that much useful. There are two reasons
Android is ever evolving technology where you will get latest Views and different options to enhance your application functionality. So using LWUIT for Android is not good choice
You can also develop BlackBerry application using LWUIT but again I would suggest to use native BB development as it provides stack of screens and many other options which are not present in LWUIT
Apart from this latest versions of BlackBerry also facilitates Android code to run on BB devices so better to go for Android development and BB development if needed
To answer your last question which is Is Java ME & LWUIT technology worth exploring? again answer is NO.
Reason for this is J2ME was developed for devices with lower configuration and with less in memory which is not the scenario for current mobile devices. and also J2ME is developed with reducing size of Java where Android has developed by enhancing Java in its own way so better go with technology which is extensible enough for the future