I don't think giganteum grows in the Dallas area, only Fat Hen and berlandieri. Were there any oaks in the vicinity? Quercus muehlenbergii? Chinkapin Oak?

Yes. They look like tree seedlings to me too. There are acorns right there in your pictures. Bet you'll find one if you remove some soil from the base of the plants.

Hmm, or maybe it's the similar Goosefoot (Chenopodium album)? There was one growing in my yard a while back...

And that "acorn" is a Pecan, so I don't think it's an Oak?

OK. I'm not familiar with pecans in the shell. But I'm pretty certain it is a tree and not an annual weed. It is 100% not Chenopodium album. Leaf shape, habit and texture are entirely wrong. I would still have a look for an acorn.

As so often your photos don't show much detail. How about showing the stem and leaf arrangement?

OK, here's a profile view..

Oak treelets. Absolutely. Dig around and you'll find an acorn at the bottom of each one.

Sure looks like something woody to me, even if it's not oak, it's def. not lambs quarters.

They should probably be pulled too, since they're so close to that wall.

Lambs quarters leaves are soft and tender and a bit fuzzy - hence a.k.a. wild spinach