Nicknamed for her Thatcheresque-resolve, Grybauskaite is tipped by most analysts to win a second five-year term as many here who remember Soviet times see her as a their best hope amid Europe's worst standoff with Moscow since the Cold War.
A former EU budget chief, the tough talking 58-year-old won round one two weeks ago, scoring 46 per cent of the vote, while rival Zigmantas Balcytis, an MEP with the governing Social Democrats, took just over 13 per cent.
No opinion polls were issued ahead of round two, which coincides with elections to the European parliament. Turnout is expected to tally at fifty percent.
Analysts say Balcytis would gain ground by absorbing the electorates of the five candidates eliminated in round one, but a majority still predict a Grybauskaite victory.
The annexation by Russia of Ukraine's Crimean peninsula and Moscow's sabre rattling in the Russian exclave of Kaliningrad have sparked palpable fear in neighbouring Lithuania, a country of three million.
"My 90-year-old aunt who the Soviets deported to Siberia believes something bad will happen," he told AFP, reflecting the widespread apprehension in the region.
Grybauskaite urged and then welcomed the arrival of American troops last month as NATO stepped up its Baltic presence.
The karate black belt also vowed to "take a gun myself to defend the country if that what's needed for national security.
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