Whenever Irelia is able to crit her spell due to Infinity Edge, Jeweled Gautlet or Jeweled Lotus; there is a bug that makes her do less damage.

Tl;dr:
Is Irelia able to crit her spell? Then the following rule applies.
The higher the % crit chance, the lower the damage of the spell will be.

For that reason, we suggest avoiding building Infinity Edge on her till this issue is resolved.

More information about this bug, is in the mentioned Leduck video.