LC is not the same as MT-RJ.
Lucent connector (LC) is a small form factor SC-style connector with RJ45-type locking mechanism developed by Lucent (now Avaya). Check out http://www.lcalliance.com for more details.
MT-RJ (not sure what the MT is, I think it has something to do with the ferrules; but RJ is short for "registered jack") is a small form factor fiber connector that features a high-density design and RJ45-type locking mechanism. From AMP / Siecor (now Corning Cable Systems). Check out http://www.mtrj.com for more details.
If you need to convert LC to MT-RJ, there are probably several companies out there who make or sell custom-ended multimode patch cables. For example, at Anixter's web site, http://www.anixter.com I searched their on-line catalog for "LC MT-RJ" (without the quotes), and got a listing of several patch cable assemblies with the ends that would do the job.
Hope this helps.