I am not at all familiar with LMB, but maybe our experience will help a little bit.
My son has dysgraphia, which lead us to an exceptional OT (I know some of the kids she has helped, and the outcomes are truly amazing). After 4 hours of screening tests, she diagnosed him with a number of issues. Her feeling is that terms like dysgraphia and dyslexia are only descriptive, they don't tell you anything about the underlying causes or how to address them. Because our son also spells terribly, and can spell (or misspell) the same word two times in the same sentence, although he reads well above grade level, she said it is likely he has some form of stealth dyslexia as well. At times he also has a repetitive (phrase based) dysfluency (stutter). But she isn't concerned with that any of these terms particular, because she believes that his OT will address all of them by focusing on the neurological issues he has.
It is unlikely our insurance will cover this, but I do know some people who have had coverage for her services. As Grinity pointed out, if you can get a referral from your primary doctor for an OT eval, that might be one way to go that has some hope for insurance coverage.
And after only a few sessions, we have seen some very positive changes in our DS. I am just glad that he can write a few sentences without bursting into tears!
Cat