Is Lambert Academic Publishing a reputable company?
No.

Publishing a thesis this way has no academic value whatsoever.  (I.e., it will lead to no prestige, respectability, credit, etc.  For academic purposes, it will not count as a published book, except for interfering with other forms of publication.)  LAP's business model seems to be collecting as many theses and other unpublished academic documents as they can and then selling printed copies.  I don't see much value to this, but it could be harmless if you do not plan to publish the thesis in any other form.  If you like the idea of seeing your thesis for sale on amazon.com, then you should investigate other options as well and choose whatever seems like the best deal.  However, it's unlikely that you'll make any money from this, and certainly no more than a small amount, so you'll be contributing more to the academic community if you make the thesis available for free online.

See also I Sold My Undergraduate Thesis to a Print Content Farm for a detailed account of LAP's business practices.