Yes, poetic justice can be ironic. That is one of the stipulations that separate it from being regular ol' justice.
Usually it is when a person gets what they deserve in the same manner in which they have given to others, for good or bad, and in a creative way. Hence the poetic.
The story where a man sells his watch to buy a hair clip for his love and she sells her hair to buy him a watch band is ironic, but not poetic justice because they did not deserve their fate.
A poor person giving their last penny to a beggar that turns out to be a rich prince in disguise searching for an honest person to name their heir, would be both ironic and poetic justice.
A ***** ******** being stabbed to death in prison would be poetic justice, but it would not be ironic. The key factor in irony is the unexpected.