Critics said any decision on extra powers for Scotland would be decided by Labour leader Ed Miliband, not Ms Lamont or her Welsh counterpart Carwyn Jones.
The Scottish Labour leader's Devolution Commission is expected to recommend MSPs be given control of the tax.
But a number of her own MPs and MSPs oppose the plans and have even threatened to boycott the party's upcoming conference in Perth in protest.
Last week, Labour's shadow Welsh secretary Owen Smith, who is close to the party's shadow chancellor Ed Balls, described devolving the tax as a "trap".
But earlier this week, Labour politicians in the Welsh Assembly backed a move that could allow the party to vary income tax rates in the future.
Last night, one of the critics of the plan, Fife MP Thomas Docherty, played down suggestions the move had given a boost to Ms Lamont's position.
He said: "This was a vote in the Welsh Assembly. But it will not be for the Welsh Assembly to decide what powers are given to the Scottish Parliament.
"Any decision to transfer further powers from Westminster needs to be taken by Westminster."