Lithuania is generally a safe country. The crime levels are on par with those in the USA. However, unlike the USA and many other countries Lithuania has no unsafe districts or ghettos and the crime is spread fairly evenly. Districts with many bars (e.g. Vilnius Old Town) may be less safe at night due to drunk people but common sense helps.
Lithuania is sheltered from natural disasters. There are no deadly earthquakes, volcanos, tsunamis, hurricanes or floods. Massive evacuation due to natural disasters is never required. Winter cold and summer heat takes some tall but mostly among the homeless.
However, history has proven that aggressive neighbors can be deadlier than any natural disasters. Lithuania stands between East and West and in 1795-1991 suffered long occupations and genocides by the great powers, primarily Russia (a third of Lithuanians lost under 1940-1941, 1944-1990 Soviet occupations alone). While a foreign invasion may still be more likely in Lithuania than in the USA or Western Europe, the chances are slim (last act of aggression took place in June 1991 when Russian soldiers massacred six Lithuanian customs officers).
On the positive side, no people have been killed or injured in terrorist bombings in the entire Lithuanian history.
While a decade ago more drivers would disobey rules and become a danger to others, campaigns against so-called "war in the roads" have curbed this (the accident rate is now similar to other European countries).
Given all of the above, the most likely nuisances for a foreigner in Lithuania are not outright crime or disasters but falling into some sort of tourist traps. Don't worry: Lithuanians are quite introverted and won't come to solicit.
That said, the group of people most notorious for cheating is the taxi drivers. A foreign tourist may be overpriced 10 times and more and some drivers are not even negotiating; out-of-town Lithuanians are also overpriced although less. Therefore it is suggested not to use taxi services in Lithuania.
In the unlikely event one gets into trouble in Lithuania and would seek outsiders' help, he/she should clearly indicate so (by asking / screaming). Lithuanians tend to be libertarian-minded and stay out of other persons' business as long as nobody gets harmed. So, for example, a streetfight is relatively unlikely to be reported to authorities (as it would be assumed that both parties want to fight).
There are some beggars in the main tourist areas (Vilnius and Klaipėda old towns) who may approach you. Never give them anything: the ones approaching tourists are not poor but rather use this as a lucrative job. They earn sums larger than an average salary as foreigners frequently hand out sums of money based on the prices in their own homeland while in Lithuania they are lower. These beggars have invented stories which they could tell in multiple languages. Take note that Lithuania is richer than most of the world; there is an effective social security system and malnutrition is unheard of.
Should you encounter problems 112 is the emergency phone number (as in the rest of the European Union).