Apartments For Rent In Lyon County Ky . Search by city, state, property name, neighborhood, or address. 3000 irvin cobb drive, paducah, ky 42003. 1206 Elkhorn Tavern Rd, Eddyville, KY 3 Bed, 2 Bath SingleFamily from www.trulia.com The median lyon county, ky rent is $374 which is below the national median rent of $1,469. There are 3 low income housing apartment communities offering 178 affordable apartments for rent in lyon county, kentucky. 209 w 33rd st has rental units starting at $1350.