Because mí is the Irish for "month", and there isn't any grammatical circumstance to cause lenition in this exercise.
Lenition and eclipsis only occur if something causes them - (usually the presence of the singular definite article for nouns, there are other reasons for verbs and adjectives). If there is no cause or "trigger" for the change, it doesn't occur.
I'm not really sure what you mean by "one of the definitions".
The Irish for "month" is mí. Mí is a feminine noun, so it is lenited afted the definite article -an mhí. That doesn't mean that mhí can be used any time you are translating month, it only means that mí is a feminine noun, and therefore it is lenited after the definite article.
in the definitions provided by Duolingo when you hover over the word being studied, there are a variety of options... I write them down so I can have another method of learning them... in one of the first studies of "month" the options for the Irish were "mi" And "mhi" ... The "lenited after the definite article" part must have escaped me! ... thank you