I know we’re talking about the recessional, but I thought I’d address both ends.
The GIRM makes it clear that the only book that can be carried in the processional is the Book of the Gospels. The Lectionary is specifically excluded, and it is mentioned that it should be at the ambo already:
*]“The following are also to be prepared … At the ambo: the Lectionary…” (118)
*]“the priest and ministers, clad in the sacred vestments, go in procession to the altar in this order: … A lector, who may carry the Book of the Gospels (though not the Lectionary), which should be slightly elevated…” (120)
*]“Then the lector goes to the ambo and, from the Lectionary already placed there before Mass, proclaims the first reading, to which all listen.” (128)
The recessional is not described in detail in the GIRM. It simply says: “After the celebration of Mass, the acolyte and other ministers return in procession to the sacristy, together with the deacon and the priest in the same way and order in which they entered.” (193) That could be interpreted to mean that, since the cross-bearer recesses with the crucifix, and the torch-bearers with candles, and the thurifer with the thurible… that the lector or deacon should recess out with the Book of Gospels.
However, the Introduction to the Book of the Gospels states very clearly that: “The Book of the Gospels is not carried in the procession at the end of Mass.” (22) That is from the 2000 edition of the Book of the Gospels.