Luke and Lorelai's relationship was contingent on one thing: coffee. It's what brought them together and the first scene we see them in together revolves around coffee. Java Junkie is just a cute substitute for the phrase coffee addict, except Java Junkie works better since it has alliteration (2 J's)
I'm not exactly sure but I believe that Java is a brand of Coffee and some people just refer to coffee as Java.. I think if that is right it pretty much explains itself.. Please feel free to correct me if I am wrong..