Those responsible for any aggression had to face "personal consequences", Lambrecht told German weekly Bild am Sonntag, adding that Germany and its allies should put Russian President Vladimir Putin and his entourage "in our sights".
"We have to exhaust all the diplomatic and economic sanction possibilities. And all further steps should be agreed with our allies," the Social Democrat said.
The comments came ahead of a visit to Lithuania on Sunday as the NATO member and fellow Baltic nations Estonia and Latvia worry about regional security after Russian deployed tens of thousands of troops near its border with Ukraine.
The trip is Lambrecht's first since being named defence minister, after new German Chancellor Olaf Scholz's Social Democrats formed a coalition government with the Greens and the liberal FDP earlier this month.
Lambrecht will meet her Lithuanian counterpart Arvydas Anusauskas to discuss the security situation as well as bilateral ties, according to the Lithuanian defence ministry.
Around 550 German troops are stationed at Lithuania's Rukla military base as Germany leads the multinational battalion in the country.
Similar military units were sent to other Baltic states and Poland in 2017 to deter Russian aggression after Moscow annexed Crimea and helped separatists take over parts of eastern Ukraine three years earlier.
After amassing some 100,000 troops near Ukraine, Russia on Friday unveiled proposals to contain the role of the United States and NATO in the former Soviet Union and Eastern Europe, calling for urgent negotiations with Washington.
The proposals called for the US-led NATO alliance not to admit new members or establish bases in ex-Soviet countries.
The West has threatened Russia with harsh sanctions should its soldiers enter Ukraine.
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