It's spelled correctly as it is. There's no historical evidence of it being spelled differently with a missing letter.
However, there are words with omitted letters in their history, like:
* "knight": originally spelled "cniht"
* "island": originally spelled "iland"
* "debt": originally spelled "dette"
These examples show how the spelling of words can change over time, but "library" has consistently been spelled the way it is.