Many high street chemists now offer exchange packs, which give you all the necessary components for cooking and hitting up heroin
However, I gotta echo what has already been said above - it doesn't really sound like you have much experience with heroin, less with intravenous use of it. Do you know anybody else who injects heroin? Have you ever seen anybody hit up?
Making the step from smoking to injecting is a big step in the wrong direction. At least when you're smoking heroin you don't need to worry about things like missed hits, abscesses, thromboses, blood borne viruses etc.
Think very hard about making this decision, as it's nearly always a one-way street. Very few people are able to go back to smoking after they have started hitting up.
And to answer the original question, again - no, lime juice is just as bad as lemon juice and vinegar for infection risk. Also, it really doesn't work very well, you need far too much liquid to dissolve even the smallest amount of heroin.
If you're determined to hit up, get to the chemist and get a 1ml pack. And for christs sake don't do it alone, do it with an experienced user, someone who will act responsibly if you go over. Many people overdose the first time they inject, not just new users, even those who have been smoking the stuff for a long time.
Watch out, yeh?