The fourth example is just plain bad. I challenge you to find a single wartime leader that hasn't downplayed their losses. You are being deeply disingenuous if you think Putin means literally zero Russian soldiers have died. It's wartime morale management 101. Literally everyone does it, including your favorite world leaders.

What I'm really after is if you have any evidence of Putin (or Lavrov, now that you mention him) lying on the scale of "Saddam is gonna nuke the West" or "NATO will not expand one inch eastward". Or has Putin ever openly boasted about his lying prowess, as fmr Secretary Pompeo and fmr Ambassador McFaul did recently? These would be convincing examples.