Is it possible to run Lua interpreter on the iphone? If yes, are there any libraries that have bindings to Iphone's SDK? If its not possible with Lua, what are the other language options?
Yes, many applications on the store (specifically games) have used Lua. However, be advised, with section 3.3.1 of the new developers agreement, calling into iPhone SDK routines from a language other than C/C++ or Objective-C/Objective-C++ is explicitly forbidden (included also is JavaScript but only on the WebKit engine, not outside of it). Therefore, if you're getting the idea you'll write your application in lua, be aware that even if it makes it through review, which is unlikely, it could be pulled at any point if you're using it for calling iPhone SDK routines.
In addition to the Corona SDK mentioned above, see also iPhone Wax.
Apple has recently revised their TOS to explicitly allow for Lua engines such as the one in Ansca Corona. So there is no need for worry about that.