Do Ukrainian citizens, who have arrived in Lithuania, have to register and is it possible to register by phone? What does registration provide?

Yes. Ukrainian citizens and their family members who have left Ukraine for Lithuania due to acts of war must apply to the registration center for registration in Alytus (Alytus, Pramonės g. 1B), Marijampolė (Marijampolė, Parko g. 9) or  Vilnius (Vilnius, Minties g. 3). Only foreigners arriving in person are registered. Once a foreigner has been registered, he or she will be able to apply for a temporary residence permit or a national visa for humanitarian reasons. After registration, foreigners who do not have a place of residence will be taken to temporary accommodation (in municipalities or with private individuals).