Why does Luke add a verse that is not there?

[Blue Bird]

Why and how is it that "and recovery of sight for the blind" is added?

It clearly isn't written anywhere in Isaiah 61.

It actually was not so clear when Luke was writing. Joseph Blenkinsopp (full disclosure: one of my professors in college) notes in his commentary on Isaiah that this phrase in the Masoretic Hebrew (פְּקַח־קֽוֹחַ) occurs only once in the entire Hebrew scriptures, thus translators would naturally have difficulty with how to understand this phrase. Even the oldest Hebrew manuscripts of Isaiah found at Qumran differ on how to write this (פקחקוח or פ֯קחקח), and that in all but one occasion the verb פקח refers to the opening of eyes, the one exception being Isa 42,20 where it refers to the opening of ears of one who does not hear. The later Aramaic Targum translates this as the uncovering of light (אִתגְלוֹ לְנֵיהוֹר). Thus one should not be too surprised that the old Greek translates this as recovery of sight for the blind (καὶ τυφλοῖς ἀνάβλεψιν), which is the same translation that Luke has.

That's an interesting thing Robrecht, I didn't know that!

It took me a while to realize your full disclosure. When I was at school, we had an exchange student from this area. When asked where she was from, she would show us the outline of Lake Michigan with her index finger and thumb and point at the joint of her thumb.