If she won't "down" without a lure it means she has not made the connection yet between the MOVEMENT of down and the reinforcement..she is simply "following her nose".
Are you using a marker or clicker? If you don't have a clicker use the word "YESSS" to mark the behaviour..which means the yes happens as soon as she is down, using the lure at first, since she obviously is still at that step in the learning process. Don't use the cue "down" yet. Just use the lure.
After using the lure for ten reps (where you are consistently getting the down) Let her sniff the treat, hold it in your fist tightly and use the exact same motion you were using with it "showing", making sure the yesss happens and the treat "opens" as soon as she hits the floor. Do another ten times successfully before moving to the next step. Use only the fist then, empty of treat (treats in your back pocket or other hand.) Deliver the treat as soon as she goes down (timing is EVERYTHING). Do ten times successfully. Take a break..do something fun and easy, like your sits or shake a paw if she knows it.
Then do the down again, empty handed, rewarding each time but tossing the treat a few feet away so she has to go over and get it and come back to you. Ten repeats. Then WAIT. See if she will come back and immediately lie down on her own. If she does, and you do this a couple of times then she understands what you want her to offer. As she offers the behaviour, add the cue.
It is much more effective in training (IMO) to add the cue ONLY after the behaviour is occurring consistently..this means the dog can learn WHAT to do before she has to learn the 'english'.
Give it a try and see how it goes. Fading the lure takes timing and practice and any time you don't get a consistent response it means the dog does not understand the next step yet and you need to take one step back, keep the reinforcement rate as high as possible, set her up to succeed (and YOU to succeed).
This should be broken up into mini sessions and try not to use the word until you are getting a consistent offering of the behaviour.