I have not heard of lead causing problems with plant growth. The levels you would normally see in a contaminated urban environment, while above human health-based levels, are not significant in terms of plant growth. It would not hurt to get a lead test so you know what you're dealing with health-wise, but I suspect something else is going on with your yard.

How is the sunlight? Do you have trees causing a lot of shade, if so what kind? Roots can also suck up water and nutrients, depending upon the species.

If you'd like to post your soil test results, there are some soil whizzes here on the forum that will look at them.

The yard gets a good combination of sunlight and shade so I don't think that's the problem. I'm debating on whether I should just add compost and lay down some grass so it doesn't look so bad but that can get pricey. I'll have to get another soil test done so I can post it here. Hopefully that will be of some help.

Be sure to take several sub-samples in different areas and mix well, then take a sample of that to the lab.

Nitrogen varies by season and isn't critical to analyze, and sometimes costs extra. I prefer to spend the $ on organic matter analysis, and micronutrients (Fe, Mn, Cu etc.) if you can. And of course P, K, Ca, Mg and pH.

Cornell University does soil testing through the Cooperative Extension Service and you can find you local office through the link below.
Lead is a heavy metal that plants do not need for growth. The problem with any lead in the soil is that it might be splashed onto the edible parts of food plants or stich to the parts of root crops we eat and then we ingest that lead. A gardener might also have some lead cling to their hands as hey work the soil, so good hygiene is essential.
What you need to know about that soil is pH (it should be in the 6.2 to 63.8 range), and levels of Phosphorus, Potash, Calcium, Magnesium, and the balance between them and how much organic matter is in the soil.
Organic matter helps, in sandy soils to fill in between the spaces between the mineral particles that make up sand and in clay soils separates the particles, hold nutrients and moisture in the soil so plant roots can more easily access them, helps feed the Soil Food Web that convert that organic matter into nutrients that plants can use to grow, and helps make soils more workable. All soils need about 6 to 8 percent organic matter to grow strong and healthy productive plants.
In addition to that soil test from Cornell these simple soil tests may be of some help,
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

You forgot the link,kimmsr.

I did didn't I.

Here is a link that might be useful: Cornell CES