this would mean "a breakfast is over" :) English has odd rules for wether you should put "the" or not, whereas most languages with a definite/indefinite distinction almost always use their articles or whatever they use to convey this meaning.
(Was that clear? :P I feel I didn't say it right)
You shouldn't be. thar is a preposition that means "over", leading us to the over=finished meaning of thart.
The done=finished meaning in English exists in Irish too, and it uses a different word - déanta, but that also back-translates as "made".
While there is some overlap (English has the phrase "over and done with", after all), the phrase "the breakfast is done" carries the implication that the cook has finished preparing the breakfast, and can now move on to the next task (Tá an bricfeasta déanta), whereas the phrase "the breakfast is over" implies that breakfast is no longer being served.
So while "done" and "over" can sometimes be interchanged in colloquial English, it's probably not a good idea to associate thart with "done".
"eclipsis" is the term used when you "eclipse" the first letter of a word, by putting another letter in front of it, just like the moon eclipses the sun by passing in front of it in a solar eclipse (urú na gréine).
"lenition" is the term used when you insert a séimhiú after a letter, to soften it. Lenition doesn't only apply to the first letter in a word.
thart isn't lenited or eclipsed. That is its basic form.
It is an old-fashioned term that is technically incorrect - the term "aspiration" describes a different phonetic process in the study of linguistics (and something else again in the study of medicine, and something else again in the study of philosophy).
The Irish for the linguistic term "aspiration" is analú, not séimhiú.