My thoughts. Based on your background, perhaps you already know some or all of these:
- Top Ph.D. schools are geared towards a research career (you mentioned teaching in your first post).
- Pubs are certainly very helpful, but not required in general for business Ph.D. admission. Finance is exceptionally competitive, so anything additional would help, but I still don't think it is an absolute or as important as other things, such as demonstration of mathematical sophistication.
- Finance requires a fairly high degree of mathematical sophistication relative to other b-school areas. I think that it would be very helpful for you to demonstrate an ability to do proofs (e.g., at the real analysis level). As far as the specific topics, diff. eqns. and random processes come to mind. I would think that the relevant courses would be available to you at LSE.
- Having a specific thesis idea in mind may or may not be a good thing. On the plus side, it could show that you've done your due diligence in the field and are clearly interested in finance. On the minus side, some profs like their students to be "malleable." I've heard this from profs, and I didn't really query them much on why this is so (I'm malleable, so it never occurred to me to ask). But from my perspective, part of the Ph.D. process is to form your research views, so attaching yourself to a specific research topic from the start isn't conducive to that. In my opinion, you'd ideally like to show that you have strong interests in a few areas and at the same time are enthusiastic about uncovering research paths in your Ph.D.