The lead piping, especially on a cold water line that old isn't really a big issue. The bigger hassle is work hardening and cracks and therefore leaks. Over the years, it develops a lining of crud, so the water isn't usually exposed to the lead. Now, some of this depends on the water chemistry, since some water chemistry can leach lead out. I wouldn't drink the stuff from the sink, though, especially if it was the 'first use'...if the line had been flushed out by running a few gallons, it should be fine. You can get the water tested, and if your ran it first to flush it, I'd bet it would test lead free. Wouldn't count on that after it sat in the pipe for hours or days, though.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013, 2014
If you could show a picture of the pipe that would help me help you.