Especially with chickens with unknown backgrounds so you are not sure of how pure their genetics are it can be really challenging to tell what you will actually get. That's one reason i like hatching eggs from mixed breed chickens, it's like Forrest Gump's box of chocolates, you never know what you will get.
That said, Lavender is a recessive gene that modifies black. Lavender will not show up in the first generation. Genetically there are a few different ways to make black but the odds are that hen is based on Extended Black. Whether or not both genes at that gene pair are Extended Black is unknown, that just adds to the possibilities. Black is pretty dominant and will cover a lot of other things. But the odds are with any of those roosters you will get either all black chicks or about half of the chicks will be black.
There is also a pretty good chance you will get leakage in the plumage. Leakage is where random feathers might show up about anywhere in the plumage a different color.
View attachment 1283354The first photo is an example of leakage I got with a black hen and a red rooster.
View attachment 1283357
The second photo shows some different leakage I got in what should have been solid white chickens.
I'm not very good at determining breeds from photos, especially of hatchery chickens. If she is from a hatchery my guess is that she is either a Black Australorp or a Black Rock, those seem to be the most common. But she could be something else or some kind of cross.