How do Jesus's Old Testament titles as Son of David and Son of God qualify Him to fulfill the demands?
The Old Testament depicts Him as the Son of David and the Son of God, establishing His kinship. By that relationship He is qualified to fulfill all demands, coming before the Father, saying He will do it, and paying off the mortgage through the accomplished work of the cross.
Les explains that God the Son is at the Father's right hand, not on the throne. When no one is able to open the scroll, God the Son comes before God the Father and says, "I'll do it. I'll pay off that mortgage." John assumes He can do it because He already accomplished the work of the cross. Les also notes that He is depicted throughout the Old Testament as the Son of David and the Son of God, so in kinship He can fulfill all those demands.