Is LuaJava a must for this? Or can I embed Lua into Java without it?
LuaJ is easy to embed in Java. I did have to change a few lines of their source to get it to work how I expected (it didn't require the IO library automatically).
http://sourceforge.net/projects/luaj/
Lua is a C library, you can embed it in Java but you'll have to interface the java virtual machine and Lua with some C code.
The LuaJava authors have already done that work - you're better off using that than writing your own.
There is http://www.keplerproject.org/luajava/manual.html, but essentially lua is more suitable for integration with C. There are a bunch of other scripting languages with good java integration around though. Consider groovy, jruby or jython for starters.
Try also kahlua and Mochalua.