East Chicago Apartments For Rent . 1 rental available on trulia. Compare rentals, see map views and save your favorite apartments. The Shoreham at Lakeshore East Apartments In Chicago, IL from theshorehamatlakeshoreeast.prospectportal.com Click on any of these properties to see photos and floor plans, read reviews, check out the. Most east chicago residents rent, and 44% of residents are homeowners. As of june 2022, the average apartment rent in lake shore east is $2,055 for a studio, $2,563 for one bedroom, $3,774 for two bedrooms, and $5,176 for three bedrooms.