It sounds like your lower back is the weak part of the chain, which is great news. Being that up in strength, and your deadlift will go up.
My lower back never gets sore. It's always my upper back.
Maybe you could add in some good mornings on deadlift day every other week on a light deadlift day. Just thinking out loud. i am a huge fan of good mornings for both deads and squats. They really helped me.
But again, if your deadlift is going up...don't tweak anything just yet. Stick with what works
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