There are instructions about removing the lectionary and Book of the Gospels from the ambo (at least when the Book of the Gospels is used with a bishop). To my mind this implies that the books are closed, not left open.
According to the Introduction of the Book of the Gospels (at
usccb.org/liturgy/innews/042000.shtml ):
"21. Then the deacon kisses the book, saying in a low voice: "Through the words of the Gospel…“33 If the celebrant is a Bishop, the deacon either may bring the Book of the Gospels to the Bishop, who reverences it with a kiss, or he may kiss the book himself. The Book of the Gospels is then reverently taken to some other suitable place.34”
So it is not correct for the Book of the Gospels to remain at the ambo. The same applies to the Lectionary, from this Introduction to the Book of the Gospels:
“PREPARATION FOR THE GOSPEL PROCESSION
10. After a brief silent reflection on the last reading from the Lectionary, or as the occasion dictates, after the responsorial Psalm, the reader removes the Lectionary.”
According to the Ceremonial of Bishops, in its description of the Stational Mass of the Diocesan Bishop:
“141. … The Book of the Gospels is taken to a side table or some other suitable place.
142. Then, all sit and the bishop gives the homily.”
(Ceremonial of Bishops, Liturgical Press, 1989, ISBN 0-8146-1818-9, page 55.)
I think closing and removing the books is also encouraged by GIRM’s mention of “special veneration” for them.
“349. In a special way, care must be taken that the liturgical books, particularly the Book of the
Gospels and the Lectionary, which are intended for the proclamation of the word of God and
hence enjoy special veneration, really serve in a liturgical action as signs and symbols of heavenly
realities and hence are truly worthy, dignified, and beautiful.”
If the lectionary remains at the ambo, it can often become a platform to put the General Intercessions on. Its removal to the side table stops this, and so helps encourage the special veneration.