The one thing that you need to know about LMB is that the same concept/lesson is taught each of the 4 hours per day. This does provide immediate review and reinforcement of the concept taught; and therefore, better mastery of that concept. However, that means that he would learn only 5 new concepts each week or 30 concepts over the 6 week span.
We have 45 sounds (phonemes), and over 100 ways to spell them. For example, there are 8 ways to read/spell the long sound of e-- e [he], ee, ea, y [happy], e-e [these], ie [field], ei [ceiling], and ey [monkey]. Thus, in order to learn how to read all of the sound/letter relationships, it will take more than 6 weeks. There was a parent on the Schwab Learning message board (no longer in existence), whose child had 600 hours of LMB.
Of course, that depends on what your child already knows, and what he still needs to learn. Consequently, the question you should ask the center is what does your child already know, and what concepts do they intend to teach him during the six weeks he will be there. Have them show you the sequence on a Student Progress Chart, and the boxes of Syllable Cards your child would be working his way through so you can see what they are talking about.
There is no doubt that LMB is a very good and successful program. However, as dhfl123 said, if you can find a good Orton-Gillingham or Barton practitioner, you could get more instruction for your money.
Unfortunately, there is no quick fix.