I will give you some information which I know about the name "Tilicki".
The name TILICKI is related to the names Tielecke, Tilicke, Thielike, Thieling, Tilichius, Thielemann, etc. which are German names. They are all variations of the German surname "THILO" (old version Thietilo). This name comes from the old German word "DIOT" which means people. In gothic people means "Thiuda".
Short forms from Thilo are the names Till, Tilo, Theo
The name Tilicki was found mostly in Schlesien and Niederlausitz which are countries in eastern Germany. I do not know the English version of these areas. Schlesien came after the second world war to Poland, but the Niederlausitz was in the German Democatic Republic (DDR) until 1990. Now there is one united Germany.
In old documents the following families are mentioned: 1327 Thilo Niger, Breslau (Wroclaw, now Poland), 1331 Johann Thilonis, DÃ¶beln (do not know where this is), 1380 Henrich Thyle zu Freiberg (Sachsen, Saxony), 1453 - 1700 Tilicke in Berlin, 1660 Casper Tilick from Breslau.
Looking through the internet, I found a lot of Tilickis in the USA. Have you any idea about these other Tilickis?
As the eastern parts of Germany have been at all times near Poland or Germans lived in the border regions of Poland or Polish people live in border regions of Germany or Germany occupied parts of Poland or Polish people came to Germany, there is of course some mixture over the last hundreds of years.
If you take as well people of the name "Tylicki" into consideration, you will find a lot of them in Poland, but as well in the USA. I do not know if they are relatives at all, but looking on the different versions of the name, it could be. I was not successfull up to now to find out if there is a relation. People in Germany sometimes call me Polish due to the name and a lot of Germans have Polish names due to their origin some generations before. The names are mostly written in a German way so that we can pronounce them, but they are since generations Germans.
Thats all for today. Best wishes - Holger