Throughout the prayers of the liturgy, e.g. the Kyrie, we often speak of and to “the Lord.” Are we referring here to Jesus, or the Father?

In the Kyrie we are referring to Jesus. This is made fairly clear in the verses, e.g., “You are the Son of God and the Son of Mary, Kyrie Eleison.”
 
However, more frequently “Lord” refers to the Father. Most of the prayers of the mass, and especially the Eucharistic prayer, are directed to the Father, through Christ. There are certain exceptions to this, in the opening and closing prayers, but in those cases, that we are referring to Jesus, rather than the Father is made clear from the wording and context of the prayer.
 
Generally, then, the Mass is understood as a prayer of Christ the High Priest, directed to his Father, and it is in Christ’s own prayer that we join.
 
Thus, with certain clear exceptions, “Lord” almost always refers to the Father.