There are quite a few options to get to ORD from Berwyn/Lyons.

If you want to take a cab, I'd suggest http://www.redcab.net It shouldn't cost more than $35.

Now, for the cheaper options -

1. Metra to Union Station and Blue Line is definitely an option.

2. Cheaper option is taking Pace Bus 311 to Oak Park - Blue line or Pace Bus 307 to Haarlem - Blue line and taking the Blue line all the way to ORD. You can find the nearest Pace stop to you at http://www.pacebus.com Cost = $1.75 (Pace) + $2.25 (CTA) = $4.00

3. Cheapest option is taking CTA all the way. You have CTA Bus 21 from North Riverside Mall. You can check other CTA buses using google maps (public transit).