My front yard is heavily lead contaminated.
I was eliminating lawn and thought it could be an opportunity to plant more food...now I know its status, I'm keeping it to ornamental plants, since they don't care about lead!
I have plenty of 'clean' garden out the back, so I wasn't going to try phytoremediation, but I did read a lot about it.
It seems to me that it's likely to take years of growing and disposing of phytoremediation plants in toxic waste dumps.
Paul Stamets has had good results with oyster mushrooms.
From what I've read, lead doesn't travel easily in plant tissue, so the further from the soil and the more processes it must pass through, the more dilute it becomes.
So roots, no way, but fruit and seeds...well, I still wouldn't.
Kids and animals are REALLY sensitive to lead. If you have children, I'd avoid growing anything in there that will be eaten.
The advice I got was to dispose of contaminated soil, and/or build raised beds. I'm generally not a fan of raised beds, but they could be your best option...not the kind of garden you envision, but a garden!

As a rule, except for the leafy things wee eat, plants do not uptake and store lead in the fruits that we eat. There is good evidence that maintaining a soil pH above 6.5 will also help. The majhor problem with lead in soil is of someone eats, ingests, that soil. Growing crops in soils contaminated with lead, generally, will not present a problem.
Because plants do not, as a rule, accumulate or uptake lead remediation by growing bioaccumulating crops does not work in lead contaminated soils. Constructing raised beds will get your gardens above that contamination, but mostly root crops (those in very close contact with your contaminated soil) would be the ones with the most lead contamination and that can be washed off.

Here is a link that might be useful: Lead in soil

I agree with kimmsr: there's very little lead movement in plants and your major danger is from lead in the soil.
I avoid contact with the soil: a really thick mulch is a good start.
But even if it's 'safe' to eat the plants from lead-contaminated soil, how would they be washed? I wouldn't want the lead leaving my place and I definitely wouldn't grow anything where I had to disturb the roots.
I'm generally pretty casual about stuff, but heavy-metal contamination's a bit beyond casual.
Of course that kind of thing has to be balance with at least you KNOW what's in your soil and can work around it. I assume there's a lot of commercial crops grown on contaminated soil...