So as much as people try denying it, English actually does conjugate our verbs. Just not to the extent of Romance languages (or even many/most Germanic languages). And one oft-hated part of foreign languages, the subjunctive, is in English as well. It’s why you can say “I were…” and still be correct. (Okay, so it’d actually be “Were I” or “If I were”) More specifically, that’s the imperfect subjunctive. (It’s the same conjugation as “Laudarem” for “Laudo, laudare”)
Saying, however, “The Lord be with you” is actually the present subjunctive (“laudem”), which is used periphrasitically as a third person imperative. Put a little less verbosely, the priest is saying “[May] the Lord be with you”, in a sense of invoking the Lord to be with this person.
Contrast with “The Lord is with you”, which is just lame old, plain old, indicative simple present. (“laudo”, or, since I can actually conjugate “esse” in the active indicative, “Dominus vobiscum [est]”)
So, in short, in the Mass, “Dominus vobiscum” is read in the subjunctive, as a sort of blessing. Even if, as ProVobis pointed out, the Lord is technically already with us. (Although I counter with the fact that the Holy Spirit is already with us prior to Confirmation, so redundancy in blessings is nothing new) Contrasting with the Hail Mary where it is read indicatively, as simply saying the Lord is with Mary.