Interestingly, in Ad Catholici Sacerdotii (which is the encyclical referenced), that statement doesn’t litterally appear in the official Latin text:
Perspicuum tamen est eiusmodi dignitatem, in iis omnibus qui eadem insigniti sunt, illam excelsitatem mentis, animi munditiam morumque integritatein postulare, quae sacerdotalis muneris maiestati sanctitatique respondeant. Hoc, ut diximus, sacerdotem constituit Deum inter hominesque conciliatorem, ex illius nempe persona ac mandato, qui est « unus mediator Dei et hominis, homo Christus Iesus ».
The official English text:
Nevertheless, it is quite true that so holy an office demands holiness in him who holds it. A priest should have a loftiness of spirit, a purity of heart and a sanctity of life befitting the solemnity and holiness of the office he holds. For this, as We have said, makes the priest a mediator between God and man; a mediator in the place, and by the command of Him who is “the one mediator of God and men, the man Jesus Christ.”
What IS literally described are: [LIST]
*]the mentis (the mind, mental faculties, translated here as “the spirit”)
*]the animi (the soul, the animator of the body, translated here as “the heart”)
*]morumque [morum] (behavior, morals, translated here as “sanctity of life”)
To answer your question though, a loft is a high place. What I would suggest is meant is that one’s spirit be of heavenly things. The Latin which is translated as lofty (excelsitatem) is a bit of an rare word, which means preeminence, loftiness, or height.