Translation:He has a difficulty with the lecture.
"deacracht" is a noun - "a difficulty".
"deacair" is usually an adjective, but it is sometimes used as where you might normally use a noun - particularly in a copular phrase like "Is deacair teanga nua a fhoghlaim" where you might expect two nouns in Irish, even though "difficult" is an adjective in the English sentence (It is difficult to learn a new language).
Sometimes it is clear cut when a phrase is a direct translation, but quite often it is a difficult call to make. In the case of the latter, it is best to defer to credible sources.
In this specific case, the exact phrase has been included in the NEID and is supported there by several examples (please see the link below). Whilst I do not doubt that there are other ways to express this, I have to accept this phrase's validity, as it has been deemed acceptable by academics whose individual and collective knowledge of the language is far greater than my own.
If you feel this is unreasonable, I am sure that the NEID would welcome your contribution (please direct feedback to firstname.lastname@example.org).
I assume its inclusion in the NEID means it is in use among native speakers, if so fair enough, but I notice there's no sign of this idiom (deacracht a bheith ag duine le rud) in Ó Dónaill, de Bháldraithe or any other older dictionary I consult. I am still inclined to think it's most likely a relatively modern borrowing from English but for the purposes of this introductory course in the Irish language this is unimportant.
The lack of its inclusion in older dictionaries may be due to the limitations of these dictionaries, as they are not as extensive in providing definitions or examples of usage as the NEID. It does not immediately follow that its absence there means that it is, therefore, an English idiom.
Dictionaries generally tend to follow language usage, albeit at a conservative distance, and the NEID is no different. I refer you to what the NEID's editor has to say on this matter below. Please see the link for the full article.
Dr Pádraig Ó Mianáin, editor of the dictionary said “the dictionary follows the trend in modern international lexicography where usage determines content. Consequently the English content in the new dictionary broadly reflects how that language is used in Ireland and the Irish content similarly is based on contemporary spoken Irish. ”
It is a moot point whether this is in the context of an introductory course: the sentence is either correct or incorrect. I am also confused by the two standards you are applying simultaneously: native speaker usage and the hypothesised borrowing. Even if we assume that it is borrowed (like a great many things), is native speaker usage not more important for teaching the language?
In summary, you are entitled to hold whatever view you wish, but in order to convince others, I invite you to provide evidence from an equally authoritative source. Otherwise, I expect that this phrase's inclusion in the largest and most modern dictionary available will reassure most people of its validity.
I expressed doubt regarding the authenticity of this phrase.
You pointed out that it's included in the NEID.
I accepted that this indicates it has use amongst native speakers. The issue as regards it's suitability for this course ends there.
(The larger question of whether this idiom originated as a borrowing from English - as I suspect - or not is irrelevant here.)
I don't think I can be clearer. That's all I have to say on this.