Apartment For Rent Oak Lawn Il . This community is located on s cicero ave in oak lawn. Nice storage, dishwasher and laundry on site. 9529 Minnick Ave Oak Lawn, IL, 60453 Apartments for Rent Zillow from www.zillow.com 5359 edison ave oak lawn, il 12 photos. Welcome to 4343 w 95th avenue & 4525 w 95th apartments in oak lawn, il. Recreational activities near oak lawn apartments are plentiful.