In Australia there are three volumes of the Lectionary. Volume 1 “Proper of Seasons. Sundays in Ordinary Time.” Volume 2 “Weekdays in Ordinary Time. Proper of Saints. Commons.” Volume 3 “Ritual Celebrations. Masses for Various Needs and Occasions. Votive Masses. Masses for the Dead.” These include the Gospel readings, but there is also another book “The Book of the Gospels”, which only has the Gospel readings.
Some countries also have a “Lectionary for Masses with Children”. The 1973 Directory for Masses with Children has:
“43. If all the readings assigned to the day seem to be unsuited to the capacity of the children, it is permissible to choose readings or a reading either from the Lectionary for Mass or directly from the Bible, but taking into account the liturgical seasons. It is recommneded, moreover, that the individual conferences of bishops see to the composition of lectionaries for Masses with children.”
The readings can be sung and the melody for this in English is in the 2010 Roman Missal. According to the General Introduction to the Lectionary “14. … On occasions when the readings are in Latin, they are to be sung to the melody given in the Ordo cantus Missae.” There is a footnote referring to this 1972 book.
While the Lectionary has a Responsorial Psalm and Acclamation before the Gospel, there are other options for this in two other Latin books: Graduale Simplex and Graduale Romanum. The General Introduction to the Roman Missal (GIRM) has: “61. … Instead of the Psalm assigned in the Lectionary, there may be sung either the Responsorial Gradual from the Graduale Romanum, or the Responsorial Psalm or the Alleluia Psalm from the Graduale Simplex, as described in these books.” I think there is an approved English “translation” of Graduale Simplex for England, Wales, Australia and Ireland: “The Simple Gradual for Sundays and Holy Days, Revised Edition”, edited by John Ainslie, published April 1970 by Geoffrey Chapman.
Lectionaries I have seen do not have music. The General Introduction to the Lectionary has: “20. As a rule the responsorial psalm should be sung. …” The GIRM has: “61. … It is preferable for the Responsorial Psalm to be sung, at least as far as the people’s response is concerned.” There are many books with different music for singing the Responsorial Psalm and Acclamation Before the Gospel.