A useful first step: underline the nouns (candidate classes and attributes) and the verbs (candidate methods).

Book: knows its title, author, ISBN, and whether it's available.
Member: knows their name and which books they have; knows whether they're at their limit.
Library: knows all its books and members; can add, search, lend, take back and summarise.

Then decide responsibilities: which class should own each rule? "Members can borrow up to three books" is about a member, so Member should know its limit. "A book that's already out can't be lent" is about a book's state. The Library coordinates: it checks the rules (asking the book and the member) and then updates both.

Errors that belong to this program deserve their own exception type, so callers can catch "a lending rule was broken" separately from genuine bugs:

class LendingError(Exception):
    """A library rule was broken, e.g. lending a book that's already out."""

try:
    raise LendingError("That book is already on loan.")
except LendingError as e:
    print("Refused:", e)

Inheriting from Exception is all it takes; the docstring says what it's for.