EssaySnark says, the LBS MIM program is specifically designed for younger students who are mostly coming straight from university. EssaySnark doesn't know about it being "right" or not for LBS to reject people with more work experience, but it's how the program is designed, and they can do whatever they want with it. EssaySnark is guessing that LBS has created this program in response to trends, from HBS (2+2) and IESE (YTP) and Yale (Silver Scholars), to catch this younger cohort. Really, they want applications from kids in their last year of university, not those who've been working for awhile, like you have. Younger business students have different needs, they need more support for career counseling, they have less to contribute in the classroom just based on that lack of real-world experience. Putting too many younger students in the same classroom as the standard MBA student is really doing a disservice to the entire class. So, it seems to us that this is a way for LBS to segregate out their offerings to better support the students all around. And, with 1.5 years in the working world, you are already in a much different position and stage of life than these MIM kids. So, think of it as a compliment!
LBS has plenty of other Master's programs for those with more work experience. Usually EssaySnark sees people complaining that "LBS requires 3-5 years work experience for their MBA program and I only have 1.5, why won't they let me in?!?"
(If that's your next question -- then sorry. You probably don't have enough work experience yet to be a strong candidate for LBS' MBA.)
Good luck with it!