Dining options in Terminal E are generally awful. There's a sit-down place near the BA gates (Cisco Bar and Grill or something like that) which serves unforgettable food at inflated prices - not recommended. There's another sit-down place right before security - it's slightly more upscale but again nothing special. My usual place of choice in E is Burrito Elito, but it's way down in the Southwest Airlines concourse (a brisk 5 min walk from the intl gates).
If you're coming from the city, I'd eat dinner there and head out to the airport around 9pm. Security is deserted at that time of night.
Otherwise, eating in the First Lounge is decent enough, although I haven't eaten there for a couple of years.