"We talked about it yesterday. I just made some kind of wish for President Trump to be as much unpredictable as possible, and even more unpredictable than with us," Grybauskaitė told reporters in Brussels at the start of the second day of NATO's summit.
"I think that any contact is okay, (it) depends very much on outcomes, but, as I said, these people are very different, very interestingly different. Hopefully, nothing bad happens," she said.
Trump and Putin are to meet in Helsinki next Monday.
NATO leaders are meeting on Thursday with the Georgian and Ukrainian presidents.
Although no decisions that would bring Georgia and Ukraine closer to NATO membership are expected to be made, Grybauskaitė said that the meeting shows the Alliance's friendliness toward these countries.
On the first day of the NATO summit in Brussels, the US president reiterated his calls on allies to increase their defense spending and criticized Germany over its pipeline with Russia.
The US president told NATO countries that they should raise their defense spending to 4 percent of their gross domestic product.
The Lithuanian said that this will depend on security challenges.
"The future is in our hands," she told reporters.
Lithuania this year plans to meet NATO's 2 percent of GDP defense spending target. To achieve this, the government may have to increase the defense budget by more than ten million euros at the end of the year.