"Irony" is a literary technique that uses one word or phrase to indicate a meaning that is the opposite of the literal meaning of the word. Something that is "lamentable" causes grief or is mournful.
So, the title of the play could be reworded to literally be "The Mournful Comedy...", which is a contradiction in terms since very few comedies cause grief and mourning. This is irony in the use of terms for the title of the play. This irony is discussed prior to the presentation of the play, as Thesus, Hippolyta, and their guests wait for the performers to be summoned.
‘A tedious brief scene of young Pyramus(60)
And his love Thisbe; very tragical mirth.’
Merry and tragical! tedious and brief!
That is hot ice and wondrous strange snow.
How shall we find the concord of this discord?
On another level, irony is present because the presentation of the play, while well-intentioned and done with a sincere wish to entertain and please the guests at the wedding celebration, becomes an almost deplorable (another synonym for "lamentable") and certainly laughable affair as the craftsmen attempting to be actors mix up lines and words and actions. Parts of the play that are meant to be tragic, such as the separation of the two lovers, become comic in actual performance, which is lamentable - too bad and a cause for grief by those who wanted to see a better quality of entertainment.