With Lydia defeated, the Greek coastal cities lay open to the Persians, who swiftly incorporated them into their empire.
Lydia was unable to be defeated, keeping the Persians out of Greek cities. 
mnli hypothesis: Lydia was unable to be defeated, keeping the Persians out of Greek cities.  premise: With Lydia defeated, the Greek coastal cities lay open to the Persians, who swiftly incorporated them into their empire.