In a general sense, you need a TO or more precise, a relationship before you can lookup a value.
In your particular case, you're constructing a join table where each new record constitutes a new fact - i.e. someone lends a book.
To do this, you join a book and a patron by setting their respective primary keys into foreign key fields in Checkout.
In short: you can't use a lookup to populate these fields because there is no connection to Patrons or Books before you set these fields.
Use a script to capture the relevant bookID and patronID into variables, go to a Checkout layout, create a new record and set the two foreign keys.
Now you could fill other fields in Checkout by looking into the two other tables.