Grass is usually really hard to kill in just a short time - it will soon start to come back from the roots, I can almost guarantee you. I suppose that if you had sparse weak grass and the chickens really scratched and pooed the heck out of it for a week it might be
mostly dead, but probably it's merely set back, not gone.
My 4x7 three-chicken tractor spent 3 weeks in one location during a busy stretch this past august, while we were in a real drought too. In that time, the spot was reduced to absolutely bare, dug, stomped pooey earth. I resigned myself to a lingering bare spot. Two and a half months later, now that it's started raining again, you can
barely see where that spot was - all grassed in again, and very green
The problem is that if your lettuce beds are trying to return to lawn, you won't get
nearly as good a crop as you could. And you will NEVER be able to really get rid of the grass just by weeding it out if its roots are well entrenched from the start.
So you might be best off turning over the ground, shovelful by shovelful, replacing each shovelful upside down so that the formerly-grass top is now on the bottom. This will bury the grass roots more deeply as well as putting the poo-iest bits way down there where they are less likely to burn the tender seedling roots or dissipate in the rain and air. Then just treat it like any other garden bed - plant, mulch, weed. By the time the surviving grass roots have made their way through all the overlying soil and any mulch you apply they will be very very much weakened and easy to exterminate permanently by hand-weeding.
This is what I've done this year to enlarge my veg garden -- left the tractor in one spot for several weeks (til cold weather made me put the chickens in their winter housing) to "discourage" the grass, then turn it upside down. I won't plant til spring because of our climate but I wouldn't hesitate to plant on the upside-down-ed soil right now if we lived somewhere warmer.
Good luck,
Pat