Hamilton had a bad weekend in Baku - the race before last - qualifying 10th, finishing fifth and falling 24 points behind Rosberg, the championship leader, who won the grand prix.
Lauda's comments caused a stir in the overworked Mercedes PR team just days after team principal Toto Wolff said his drivers were 'brainless' to have crashed on the last lap in the following round in Austria last weekend.
Mercedes downplayed Lauda's comments, saying that, although Hamilton was angry, the room was not 'destroyed'.
Referring to Hamilton's claim in a recent Mail on Sunday interview that his relationship with Rosberg is 'really, really good', Lauda said: 'Lewis lied about that, simple as that.
'He just said something. He wanted to be the softener in order to have his peace last weekend (in Austria).
'He does what he can. The fight gets hotter the longer Nico is in front.'
Lauda's comments were recorded before last Sunday's race, where Hamilton won after Rosberg barged into him on the final lap, damaging himself. The German finished fourth to see his lead cut to 11 points, as Mercedes bosses shook their heads in annoyance.
It was the third time this season the pair have collided. Now Lauda and Wolff are threatening to introduce team orders - telling their drivers not to race against each other but to fit in with what is best for the team.
-Daily Mail