What are the clinical indications for performing a second laser peripheral iridotomy (LPI) instead of proceeding directly with cataract surgery?  

The only reason for a second LPI in CACGL or occludable angle is if sector iris bombe develops due to posterior synechiae formation. Otherwise, one LPI will normalize the pressures between the posterior and anterior chambers. If you still see progressive angle closure after LPI, you are dealing with...

Perform cataract surgery.

If there is appositional angle closure, then lens removal makes sense, but I have seen angle closure with deep chamber, then Omni/GAT with TRab BYPass stents (MIgs) help recover angle performance. I have done it as a standalone without concomitant CE/IOL surgery, to the great benefit of patients.