Deadlifting in runners is seldom a good idea; the cushioned sole leads to instability under load, but worse than is the elevated heel on the standard running shoe which shifts our weight forward during a deadlift.
If our weight shifts forward we need to drop our hips lower to prevent ourselves tipping over. Dropping our hips drives our knees forward and leads to the quad-dominant 'squatting' deadlift referenced in other posts of mine, and means the barbell must also move forward to clear our protruding knees.
The further the barbell is from our base of support, the greater the shearing force through our lower back, and 'bad' pain is often the result.
The symptoms Natalie reported all fit in with this dysfunctional movement pattern, thus my suspicion she was wearing runners for her deadlifts. Elementary, dear Watson.
I suspect poor glute engagement will be the major culprit here and will be addressed at our next session, but the first step will be to ditch the runners. Shoes off for deadlifts, people!