Gazprom, which already holds stakes in gas companies in both Latvia and Estonia, is the sole bidder for the stock.
A tentative deadline of Nov. 12 is set to make a final offer in the tender, which is due to be concluded by the end of the year.
Under conditions set for the tender, the potential investor must guarantee gas supplies for 10 years and satisfy 70 percent of Lithuania's needs.
In May, a 34 percent stake in Lietuvos Dujos was sold to a consortium of German Ruhrgas and E.ON Energie, which paid 116 million litas (33.6 million euros) for the package and pledged another 70 million litas in investment.
Lietuvos Dujos earned 42.5 million litas in pre-tax profit in the first half of 2002.
After privatization, the government will hold a 24.36 percent stake in Lietuvos Dujos.
Lithuania had long resisted Russian investment for fear of over-reliance on Russian energy.