Hey Dennis,
A good starting point for comparing graduate programs in terms of relative strengths by field, probably the best place to start is:
http://econphd.econwiki.com/rankings.htm
Now it's by literature productivity, so it's not a perfect ranking (i.e., it doesn't take into account quality of placements, support for grad students, etc). But it's a good starting point.
A similar type of study can be found here:
http://www.econ.uconn.edu/Ranking.pdf
But it only sorts by JEL classification code.
As for your question about time required to complete the degree, in most cases you will not receive academic credit for any of the courses that you completed at LSE and you'll have to complete the same requirements (core course, field course, etc). That would still be the case even if you were coming into the school with a MSc in Economics from a top school (as LSE obviously is). Now it's possible that you will be able to complete your research in less time than many in your cohort because you have a clear idea of what you want to study and probably a better understanding of how to successfully complete academic research than the typical student starting a PhD right after completing his/her undergrad degree. I'll be starting my PhD Economics this fall with a MA Economics (from a state school nowhere near as good as LSE) and I'm hoping to be able to complete the PhD in 4 years (mean is ~5.5 years).