No, the Gospel Reading is
not part of the Liturgy of the Eucharist.
It is part of the Liturgy of the Word.
The Mass is typically divided into two main parts:
* Liturgy of the Word: This includes readings from Scripture (Old Testament, New Testament letters, and the Gospel), the Responsorial Psalm, the Homily (sermon), the Creed, and the Prayers of the Faithful.
* Liturgy of the Eucharist: This includes the Preparation of the Gifts, the Eucharistic Prayer (including the consecration of the bread and wine), the Communion Rite (Lord's Prayer, Sign of Peace, Lamb of God), and Communion.
Therefore, the Gospel Reading belongs to the first part, the Liturgy of the Word.