How does Luke 11:5-13 fit as corollaries to the Lord's teachings on prayer [Luke 11:1-4]? I find Luke's account of the Lord's prayer model for His disciples revealing:


God's familial relationship with us as He is introduced to us as OUR FATHER who is to be hallowed...
and secondly
God's providence as we are asked to petition Him about His kingdom, our daily bread, forgiveness and temptation.


How then does the story of the midnight traveler and the father-son illustration in Luke 11:11-13 serve as corollaries expanding on the content of the Lord's prayer?
Jesus appended the illustrations of a midnight request from a friend, and a father never giving his child a bad thing when asked for a good thing, to encourage his disciples to ask God as Father who is also a friend.

However, there may be a problem grasping the application to ourselves if we simply assume that God is our heavenly Father. Bear in mind who Jesus was speaking to - his disciples, all of whom were Jewish people in covenant relationship with God, the Yahweh of the Old Covenant (or, Testament). They already knew God as their heavenly Father, and that he viewed them (and all Israel) as his covenant people, bearing his name. That entitled them to address God as 'Father'. But the pagans could not do that! You had to be in God's covenant to have that close relationship with him before you could call him 'Father' or 'Abba'. Romans 8:14-16 explains this by saying to Christians, 


  "For as many as are led by the Spirit of God, they are the sons of
  God. For ye have not received the spirit of bondage again to fear; but
  ye have received the Spirit of adoption whereby we cry, Abba, Father.
  The Spirit itself bears witness with our spirit, that we are the
  children of God..."


It might be worth suggesting that only when that situation obtains with individual believers can they grasp the significance of what Jesus was saying about praying to God as "our Father". Then we will hallow (or, revere) God, and then we will be bold to persist in asking him for good, and correct things. We will know him to be our loving heavenly Father, and also our friend.

The story of the midnight traveler and the father-son illustration in Luke 11:11-13 are then clearly seen as the warp and the woof of the one cloth of praying to God as Father and as friend. There was no need for Jesus to mention what I have mentioned to his disciples as they already knew their standing before God as children of his covenant, but there might be a need to mention this today as not all who assume God to be their heavenly Father might yet be sons of God. They have to be brought into the New Covenant Jesus instituted the night before he died: 


  "This cup is the new testament [or, covenant] in my blood, which is
  shed for you." (Luke 22:20)


I hope this is helpful in grasping the immense significance of those corollaries in boldly petitioning God in prayer, as Father.