I published my Ph.D. dissertation using ProQuest because it was the service authorized by my university. But I don't regret it, it was a great experience that offered minimal risk regarding upholding the quality of my research. The service is more professional and not predatory like Lambert Academic Publishing. The good thing is after publishing with ProQuest, I published one of my chapters with Water Research and I am editing another chapter for publishing in another top journal. Publishing with Lambert Academic Publishing you forfeit your rights to your work and your work rots on their catalog with zero to minimal recognition.
As stated earlier the authors keep the copyright of their work; additionally authors are paid a royalty for sales in all formats. ProQuest is extensive and global archive. If the university does not participate in ProQuest Dissertation and Theses Dissemination program, one can still submit the work.
I don't find any real disadvantage.It may be mentioned that ProQuest submission is equivalent to e-repository submission, and there is no peer-review process.
I also suggest that you make the effort to talk to colleagues about the choice of the best serious scientific publisher. Publishing houses like Springer, Wiley, and several others have quite many book series, which means that you can target the right audience by choosing the right series - if, of course, the quality of your work is sufficiently high. You may perhaps also send along some recommendations from your thesis committee members, supervisors, et al, so as to convince the publisher that it would be worth while for them to publish it.