I’ve only ever seen exposition of the Eucharist in churches and chapels, but today I was looking at the website of a parish that said they have Eucharistic adoration in a room in the religious education building. Is that licit?
It has to be done in a church or chapel (that is, an actual dedicated chapel, not just a room that people call “a chapel”)–I say this because the liturgical documents clearly presume that Adoration is being done “at” the tabernacle or at least within a church (or oratory, or chapel) However, the bishop can give permission for it to be done in any dignified place.
According to canon law, the bishop alone can give permission for a tabernacle. When a church is dedicated as a parish church, this is a given (since that’s part and parcel of designating it as a church). Anything other than a parish church requires his permission.
We don’t know whether or not the bishop gave his permission for what you’re describing, so whether or not it’s licit is likewise an unknown. Even without his permission, it might possibly be licit.
Parishes can certainly hold Eucharistic processions, even those that are outdoors, so there’s no rule that the Blessed Sacrament “must” remain within the walls of the church.
If the priest is taking the Blessed Sacrament from the tabernacle in the church and placing It for veneration in a dignified place in the RE building, I don’t think there’s anything specifically prohibiting such a thing, but common sense tells us that it shouldn’t be done in any place not befitting the dignity of the Body of Christ. The simple description “a room in the RE building” might be anything from a prayer-room that’s used for no other purpose, to something that looks like a large broom closet.
That’s a long way of saying that I personally don’t think this is really a question of “is it licit?” as much as “is it proper?” And I think that really depends upon just what type of room is being used (is it dignified enough???)
EUCHARISTIAE SACRAMENTUM in #12 says the following:
c. There should be an opportunity for common prayers and extended adoration in the presence of the blessed sacrament exposed at designated churches that are especially suited to this form of piety.
ewtn.com/library/CURIA/CDWSACRA.htm
That’s in reference to Eucharistic Congresses, which isn’t exactly what you’re asking about, but it does make the point that the proper place for Adoration is indeed a church.