where can I send a backyard soil sample for lead testing?
It seems that this document answers most of your questions:  

Testing for Lead

In the document it states that home kits are available, but it has been shown that the effectiveness is not too reliable, and if you do detect lead, you will probably need to get soil professionally analysed.

otherwise you can find do-it yourself test kits on this link if needed.
DIY Test kit

Personally, I would inspect the soil for any traces of paint chips and if you find any, then get lab tests. however a sensible course of action would be to order in some top-soil for your garden, that way, your garden will look nice in a few weeks and you will have peace of mind in terms of contaminants.