We've just bought 2 Fire Tablets and are setting them up, but can't figure out how to get rid of the obnoxious search bar that shows up smack bang in the centre of the lock screen. I've tried the only suggestion I could find, which recommended turning off the notifications for Unified Search but that did nothing. The lock screen still has that ridiculous (and pointless) search bar smack across of the middle of the screen, obscuring the wallpaper. I can't even find a way to move it to, say, the bottom of the screen so it's less prominent. I'd rather a way to get rid of it compeltely, but at least knowing how to move it would be something.
How to remove the SEARCH BAR on the Fire 7 tablet LOCK SCREEN. I finally figured it out! On your device go to Settings/Device Options/Search Bar. You'll see "Display search bar on lock screen". Set it to the off position. No more dumb search bar!
(I never had a lock screen search bar on my Fire HD 8 tablet, but out of curiosity, I looked to see if this setting option existed in the same place. There is no Search Bar/Lock Screen setting under Settings/Device Options.)