Over the last few weeks, the retired general has issued several thunderous warnings about the consequences of Nato expansion, but he struck a more moderate note when he prepared yesterday to meet his former Cold War foes.
He looked forward to a "complicated but civilised dialogue", he said, although he added that details of his new proposals were for the ears of Javier Solana, Nato's secretary-general, whom he meets today.
Nato officials have been stressing that Mr Lebed is on a fact-finding trip which is part of a wider policy of closer contacts with Russia, a move which reflects their anxiety to play down the importance of the meeting in case it goes wrong.
In recent weeks, Nato has been receiving mixed messages from Russia, not least because Moscow's senior officials tend to be more damning at home than they are in the West. Although Russia has consistently opposed Nato's plans to expand into Hungary, Poland and the Czech republic, Moscow has wavered be- tween the conciliatory and the hardline.
The hospitalised Boris Yeltsin recently indicated that he wanted a treaty with Nato which would govern Russia's relationship with the alliance, before it goes ahead with expansion - a suggestion which met with approval within Nato. And his foreign minister, Yevgeny Primakov, has stressed that he does not want the expansion issue to threaten co-operation between Russia and the West.
The defence minister, Igor Rodionov, last week suggested that arms reduction agreements would be in jeopardy if Nato pressed ahead with its plans, which most Russians see as a throwback to the suspicion and hostility of the Cold War. He called for the alliance to transform itself into an international peace-keeping organisation, under the United Nations.