Shares in the 39% state-owned bank rose above the 61.2p level at which the Government said it would break even on its 2008 bailout, and are now at their highest point for two years.
The Treasury is widely expected to begin selling its stakes in Lloyds and 81% nationalised Royal Bank of Scotland before the 2015 general election. Prime Minister David Cameron recently raised the prospect of selling RBS shares at a loss.
Shares in Lloyds have more than doubled over the past year, boosted by state stimulus for the banking sector, the recovering economy and housing market, and its improving balance sheet.
Lloyds chief executive Antonio Horta-Osorio on Thursday told shareholders at its annual meeting: "We expect us to return to profitability this year and to grow our core business, to realise our full potential to deliver strong, stable and sustainable returns for you, the shareholders, and to allow UK taxpayers' investment in the group to be repaid."
However, the 61p price has been described as "contrived" by banking analyst Ian Gordon at Investec Securities, who argues it "conveniently ignores its average in-price of 73.6p".
The state ploughed more than £20 billion into Lloyds at the height of the credit crunch after the then Labour government brokered its rescue of Halifax Bank of Scotland.
Lloyds remained in the red in 2012 with pre-tax losses of £570 million after setting aside £3.6 billion to compensate customers who were mis-sold payment protection insurance (PPI). But its first quarter underlying profits surged to £1.5 billion, with bad debts plunging by 40%.
Lloyds chairman Sir Win Bischoff recently announced he is standing down and hailed ''significant progress'' in the bank's recovery. UK Financial Investments, which manages the state's bank holdings, declined to comment.