I would definitely apply but I'd advise you to pick a back-up program as well. You can apply for 2 programs (or even more if you're willing to pay the fee again), so if you don't get into IR you'll be considered for your 2nd option too.
As far as my situation, I had a 3.42 GPA from a good university, with work experience and multiple languages, I applied in late November and I didn't get into IR but was accepted to my 2nd choice, Comparative Politics. In the end I'm happy with it as the courses are similar and I get to specialize in Conflict Studies, which is what I'm interested in.
Generally the 3.5 minimum is not an absolute requirement, but because the MSc IR gets so many applications, you will have to put together a very good application to have a chance. Your academic qualifications are the #1 factor that LSE is going to consider so do everything you can to prove to them you will be capable of doing the coursework- whether through your letters of recommendation, your personal statement, etc. I'd also recommend applying as soon as they start accepting applications in September or October. Let me know if you have any more questions about LSE as I'll be starting there in a month or so.