A couple of things:
It's possible that the food can be part of the issue. Free feeding definitely has to go, it makes it terribly difficult to work on housetraining when you can't predict when she might have to "go". When you feed on a schedule, that part of the housetraining thing gets easier. Also, it is possible that she is sensitive to grains or to something in the food. It is by no means universal, but some dogs can have real serious issues with the artificial ingredients in some dog foods. You may want to ask your vet about it and possibly try a new food if feeding on a schedule doesn't resolve the inconsistencies in her pooping.
It's also possible that she is unsure of how to communicate to you that she needs to go outside. In my own experience, I tried many methods (and cleaned a lot of poop!
) until finally being given the advice to teach my dogs how to ring a bell on a string when they needed out.
Keep being patient with Luci and be a good leader for her. She has probably had quite a lot of inconsistency in her life up till now and she really needs her new people to help her understand what to do.