If changes are made to the data in an app being referenced by a Lookup field, it will not update values that have already been retrieved by the Lookup field.
The most efficient way to update data in existing records is to update the records in bulk by importing a CSV file.
If you bulk update the values in a Lookup field by importing a CSV file, the values retrieved by the field's field mappings will also be bulk updated.

Note, however, that values cannot be updated if the field selected as the Key field contains duplicate values in the datasource app, as the target record cannot be uniquely identified during file import.

For details on how to bulk update the values of a Lookup field using a CSV file, refer to the following page.
Is it possible to import values from a file into a "Lookup" field?