IIRC the level after running the water for 5 min in the morning was around 1 PPB, so not high enough to freak out about, but not zero. I just generally assume that I should not give my kids water straight from the tap, because the level _could_ spike for various reasons like them working on the water main, etc.
As someone else pointed out, Chicago has made some changes here - and they plan to eventually remove all service lines. That said - this is Chicago. The mayor had a goal to remove 650 lines this year and there was a story in the Chicago Tribune recently that so far that number is ... 3. For context there are ~400k lines to replace.
The OP mentioned that this was a few years ago. Things are different now. Literally one month ago Illinois became the second state to legally require all lead pipes to be replaced [1]. I do believe that the Chicago city ordinance of last year waives all permitting fees now. I am not sure how it is going to be paid for: public money? homeowner pays?