WE are only reading Luke and reading the whole chapter, which is 3 stories about Lost and Found.  (Really the parable is the story of a lost son and prodigal father).

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Here is where I get to share something from one of my many files.  For your enjoyment I hope.

Variations on The Prodigal in the key of F       

 Feeling footloose and frisky, a feather-brained fellow
 Forced his fond father to fork over the farthings.
 And flew far to foreign fields
 And fabulously frittered his fortune with faithless friends.
 Fleeced by his fellows in folly, and facing famine,
 He found himself a feed-finder in a filthy farmyard.
 Fairly famishing, he fain would've filled his frame,
 With foraged food from fodder fragments.
 "Fooey, my father's flunkies fair far finer,"
The frazzled fugitive forlornly fumbled, frankly facing facts.
Frustrated by failure, and filled with foreboding,
He fled forthwith to his family.
Falling at his father's feet, he forlornly fumbled, "Father, I've
Flunked, and fruitlessly forfeited family fellowship favor,"
The farsighted father, forestalling further flinching,
Frantically flagged the flunkies.
"Fetch a fatling from the flock and fix a feast."
The fugitive's fault-finding brother frowned
On fickle forgiveness of former folderol.
But the faithful father figured,
"Filial fidelity is fine, but the fugitive is found!
What forbids fervent festivity?
Let the flags be unfurled! Let fanfares flare"
Father's forgiveness formed the foundation
For the former fugitive's future fortitude!

We're having communion this Sunday so I think I'll go with the 'surprise party' theme, talking about God's surprising grace in welcoming us home, and all of us being welcomed to the banquet, no matter where we've been and what we've done, we are forgiven and invited. Surprise!

Reading all 3 parables does seem like a good idea. As you say, they are all about Lost and Found. I suppose one difference is that the sheep and coin do nothing to be found, but the son has to at least "come to his senses" and head back towards home.

Somewhere I read a suggestion that the prodigal parable could be called the parable of TWO lost sons, since the elder son seems to have lost his way too at some point. The father invites both of them to return. (Probably that's from Henri Nouwen's book, the Return of the Prodigal Son.)