What to do with concrete/cement runoff from cleaning tools?
Definitely not on the lawn! The water is caustic and can have a high pH value 10+ etc. 

What I do is let the water settle. My process is as follows. I wash my mixer and tip the water into the wheelbarrow. Then I scrub the wheelbarrow and then tip the water into a rubber bucket. Then I wash the hand tools in this bucket, rinsing with a little extra fresh water into the same bucket. 

So, now you have a pretty full bucket of dirty water. Leave it overnight (or longer). The solids will settle to the bottom and leave pretty clean water on the top. I usually tip this onto a gravel area if there is one (scrape back the top layer with your boot, pour and once it soaks in, push the clean gravel back over). 

Then you're left with a third of a bucket of dry/set sand/cement mixture which you can scrape or knock out of the bucket and dispose of with your other 'hard' waste, brick off cuts etc.

Hope that helps.