Because Grand Duchy of Lithuania and modern Lithuania had a very different ethnic composition. The GDL started from territories of modern Lithuania, but next (after disintegration of Mongol Empire) they conquered former ruthenian principalities that had ruthenian Ortodox Slavic population. The nobility of Lithuania first Ruthenized and next Polonized. The official language of GDL was ruthenian. Modern Lithuania and lithuanian nation were created in XIX century from peasantry who lived on territories of today Lithuania. Most of former GDL become Belarus, who was heavily russificated after partiitions of Poland. So - Grand Duchy of Lithuania was a ruthenian state with lithuanian ruling class (who next rutheanized). Lithuanian peasants didn't change the language and in XIX century they developed nation who gained independence in 1918.

Is that map also correct in saying that Genoa Italy ruled Crimea?

Samogitia, the western half of Lithuania and the portion on your map controlled by the Teutonic Knights, was the stubborn final holdout of pagans in eastern Europe. As a result, the Teutonic Order and the Livonian Order engaged in constant attempts to expand their mission there militarily. Lithuania managed to rebuff their attempts and simultaneously expand to the east and south, but the region did switch hands frequently, so your map is one of the times in which it was not occupied by Lithuania.

As for the rest of Lithuania, it should be noted that just because Lithuania had annexed those regions does not mean that those places had a Lithuanian-speaking peasantry (or nobility, for that matter). Most of "historic" Lithuania was Belorussian or Ruthenian, and the borders of modern Lithuania fairly accurately represent the actual borders which contained Lithuanian language speakers in the medieval era.

As a follow up question, why is Macedonia in a completely different place than the ancient Macedonia?

OP, can you link to the map? I don't have any knowledge about what you're asking, it just looks interesting.

Was there much change in the cultural identity of the people in this region during the early part of the 20th century (post WWI)? I ask because I've come across conflicting reports in my own genealogy. While official records place my ancestors in modern day Lithuania, some records claim that they're actually Russian while others report them as being of Polish decent. I don't have specifics unfortunately as even records from Ellis Island are incorrect.

The map is incorrect. Žemaitija (a.k.a. Samogitia) was a part of GDL.