If you know the name of the parish owning or associated with the cemetery where Freda is buried (assuming she was Christian and not Jewish or Russian Orthodox), then that information coupled with her approximate year of birth should be enough for the Historical Archives to do a search of that parish's records (assuming they still exist). The following are the names of the RC churches in Alytus:
ALYTUS. S^v. Angelu Sargu [Church of Holy Guardian Angels or Guardian Angels]
Savanoriu g. 14 [g.=gatve, street – the dwelling number follow the street name]
LT-62142 Alytus [this is the postal code]
tel. (315) 5 22 38
ALYTUS. S^v. Brunono Kverfurtiec^io [Church of Saint Bruno of Querfurt, or of Saint Boniface]
Putinu g. 20
tel. (315) 2 79 87
ALYTUS. S^v. Kazimiero [Church of Saint Casimir]
Varenos g. 24a
tel. (315) 5 10 19
ALYTUS. S^vc^. M. Marijos Kriks^c^ioniu Pagalbos [Church of the Virgin Mary, Help of Christians]
Jurgis^kiu g. 4
Tel. (315) 2 55 52
Sacramental records (baptism/birth, marriage, and burial/death) are now centrally held by the Historical Archives of Lithuania, not the Central State Archives. The web page for these Archives is in English here:http://www.archyvai.lt/en/accessandservice.html
It includes the email address. You can write them with an inquiry to provide you with a translated (into English) copy of Freda's birth, marriage and/or burial record (if these still exist and are not held by the Polish Archives.)
If you have not given them enough information to do a search, they'll tell you. If the records no longer exist or cannot be found, they'll tell you that. If they find one of these records, they'll tell you that and tell you how much it will cost to do the search and translation and how to send the fee to them. Alytus is one of the larger towns in Lithuania (about 60,000 today and around 3445 in 1897). If the Archives sent you the wrong records, I would let them know that fact and ask for a new search with a translation into English.
Most cemeteries in Lithuania do not have any records of burials nor do local churches since the Soviet period when such records were centralized into the Historical Archives. Local grave diggers also do not know where individuals are buried except randomly. Most older graves (e.g, pre-1900) are unmarked though some local people may know where some individual graves are located. Most local priests do not speak or understand English.
If I were you, I'd try getting the naturalization papers of all the children you know of, plus any Social Security applications they may have filed -- both of which documents often have the name of the village where the person was born.