Advantages and disadvantages of doing PhD research at a non-academic lab
Throughout graduate school I worked at and was funded by a university-run laboratory that operated somewhat like a government laboratory and was largely funded for applied research. I now work at a UARC (which is similar to an FFRDC).  Given that my graduate school lab was already affiliated with the University, though, my situation is slightly different than yours.

At least in the US, it is relatively hard for non-academic laboratories to find funding for basic research; funding agencies like the NSF have a prejudice toward funding degree-granting institutions.  Therefore, in my experience, much of the flavor of the funding at non-academic laboratories is geared toward applied research.  This might not be a problem, but it can be a challenge to find a deep, Ph.D.-level problem to solve when your sponsors are interested in seeing more concrete results.

In my case, working at an applied research laboratory to fund my graduate degrees was actually somewhat of a benefit.  Due to the reasons I listed above, it was difficult for me to latch onto a deep problem to solve for which there was stable, direct funding.  Therefore, I used my position at the laboratory to basically "pay the bills" (it covered my stipend, tuition remission, &amp;c.).  That gave me the freedom to work on related—but not directly funded—problems that interested me.  This of course had the overhead of essentially working two jobs at once, but it had the added benefit of providing visibility to my "side" research to the sponsors who were funding my "pay the bills" research.  It also paid for my trips to relevant conferences, at which I was able to present both flavors of my research.

Now that I am working at a UARC, I see others here who are also pursuing part-time Ph.D.s.  Most of them seem to have found a similar model to mine: They use their position at the non-academic lab to "pay the bills", and then focus their actual research on a related but independent problem.  If you are able to fund yourself (i.e., if your Ph.D. advisor doesn't have to worry about finding funding for you), then many advisors will be willing to take you on as a student.