Describing Michel's approach as "brazen", Lamb said the lobbyist had wanted "things to run smoothly" with the Sky bid, but warned that "if it goes the wrong way" he was "worried about the implications".
The note added: "It was brazen. VC [Vince Cable] refers bid to Ofcom, they turn nasty."
Lamb claimed that the threat was offset with an enticement should Cable allow the Sky bid to proceed unhindered.
He said that it was proposed that The Sun would help persuade voters to back the Lib Dem's alternative voting (AV) system of proportional representation, which had been key to the party's coalition deal with the Conservatives.
Lamb told Lord Justice Leveson that got a "very clear understanding" from the meeting with Michel that News Corp's UK newspapers had been supportive of Lib Dems in the past, but that positive coverage could change quickly.
The note's final sentence says: "Implication was clear, News Int turn against coalition and AV [if bid does not go through]".
In another note, Lamb said that Clegg had been "horrified" to hear what Michel allegedly said in the meeting. Clegg is said to have fretted: "We will lose the only papers who have been positive."