I've added an offset to lap, place. Place and Lap are still visible in the pause menu when switching to practice after race. Maybe Joe can look into it.
Fixed in 3067. The HUD was getting Show() called on it when entering the pause menu, but Update() doesn't get called when the sim is paused, so items had the wrong visibility until the game was unpaused. Now the visibility state is cached in the HUD and calling Show() when the HUD is already visible does nothing.