My mom works for our local municipal government administering a HUD lead abatement grant. The state of lead contamination in many older homes in low income areas is just awful.
If you are on well water, call your county department of health, there might be a fee, but it should be lower than a private lab.
I'd expect them to work reasonably well, at least for lead. The chemistry is pretty simple. Whether they can detect low concentrations is another matter. You could boil a pot of water until most of it is gone and test that. You'll have a much higher concentration of any contaminants.
An example: https://www.homedepot.com/p/Safe-Home-Do-it-Yourself-Lead-in...