Probably there are three circumstances provided in this Article where LG can act against or independent of opinions of Ministers of Delhi.
1) About specific matters within discretionary powers of Governor
2) Matters on which he differs with Ministers of Delhi.... Here he will ask opinion of President, and while awaiting opinion, he can decision against wishes of ministers if there is emergency.
3) Regarding 3rd Circumstance, "Silence of Constitution provision" applies. What to do if Ministers just keep sitting on file, neither agree nor disagree..... Here also LG has power to take decision assuming either implied consent of ministers or assuming implied disagreement of ministers. In both cases he has power to take decision independent of advice of ministers.
This is of course my personal view. Please check Article 239AA (4) Proviso, itself for authentic view. I have not come across a precedent on this issue.
Haresh Raichura
16th May 2015