Lucy, no problem at all. Łyko, Łyczko, Łyczek, Łyczka,Łyczyna, Łykowa, Łyczanka, Łykówna, Łyczkówna, etc. are all variants of the same name. And Łuczak in one of the later records was the priest’s error. Unlike English and like most Slavic languages, Polish has rich inflections and very creative word formation. One of the characteristics is the formation of diminutives by means of special endings: -ek for masculine nouns, -ka for feminine and –ko for neuter, often accompanied by consonantal alternations, e.g. dom ‘house’ – domek ‘small house’, noga ‘leg’ – nóżka ‘small leg’, oko ‘eye’ – ‘oczko’ ‘little eye’, etc. The ending can sometimes be doubled: kot ‘cat’ – kotek ‘kitten’ – koteczek ‘small kitten’.
In older Polish this also referred to surnames/nicknames. If Jan Nowak had a son, the boy could be baptized as e.g. Adam Nowaczek or Nowaczyk 'little Nowak'. When the boy grew old, the diminutive variant either remained or was replaced with the original form, so he could be both Adam Nowak and Adam Nowaczek. Very often brothers had different names and it also varied in further generations without any consistency whatsoever. One of my maternal 3rd great grandfathers was Andrzej Kozieł, his son was Franciszek Koźlak but my great grandmother was baptized as Ludwika Kozieł. And as I wrote yesterday, sometimes the ending -ski was added: one of Ludwika's brothers was baptized as Kozłowski... Thus Łyczek was the perfectly regular diminutive of Łyko.
With women’s surnames it was even more complicated.Depending on the final syllable of the husband’s surname, wives took endings –owa,-ina, -yna and colloquially also –ka, again often accompanied by consonantal changes, so Mrs. Nowak could be Nowakowa, Nowaczyna, Nowaczka, Mrs.Noga – Nogowa or Nożyna, Mrs. Mucha – Muchowa, Muszka, Muszyna, etc. Daughters took endings –ówna, -anka, -onka, so Miss Nowak was Nowakówna or Nowaczanka, Miss Noga – Nożanka or Nodzanka, etc. This system, however, gradually disappeared from usage in the 20th century and nowadays it can only be found in some rural
areas and, interestingly, among some artistic and scholarly circles – some actresses and university professors still use the feminine form of their surnames ending in –owa, -ówna, -anka, though in their documents the basic masculine form is now obligatorily used. The only exception are surnames ending in –ski, -cki, where -i has to be replaced with –a, so Anna Kowalska is the only acceptable form in both official and colloquial usage. Anna Kowalski would only be possible for women born or married abroad, who were registered as such in foreign documents.