[TheBigBoy2000]

I am a graduate student and  my topic is this: http://pubs.acs.org/doi/abs/10.1021/jo5001803.

I would like to carry out this reaction using a Chiral Lewis Acid to preserve the Axial Chirality. Does anyone know of a Chiral Lewis Acid Catalyst that will achieve this?

[discodermolide]

Sorry in that abstract I don't see axial chirality being presented.
But there are plenty of axially chiral phosphoric acids around.

[NiceWeatherSunshine]

Is this in regards to controlling regiochemistry for the cyclization with  meta substituted phenyls (the ring shown to be R3 substituted in the abstract)?

if you look at table 2, it seems like there aren't problems with that ring rotating fast relative to the cyclization rate. well, at least the authors didn't report nmr data that indicates they isolated more than one 7-exo-dig cylized isomer, at least for the conditions then ended up putting in the paper. i think the chemical shifts are right for the regioisomer they showed.