I am confused. Shouldn't the sentence be "My lubie ciasteczka." Its like having we in the sentence twice; My and lubimy.
no. that would be something like "we likes" or "we am"
"lubimy" is a form of "lubić" =to like , that goes with "my", no other form can be used with "my" (in present tense).
But because "lubimy" already contains information about "my", it is unnecessary, and is usually omitted, unless you want to make a point that it's us who likes cookies.
(ja) lubię= I like
(ty) lubisz= you like (1 person)
on/ona/ono lubi = he/she/it likes
(my) lubimy= we like
(wy) lubicie= you like (2+ people)
on/one lubią = they like
I always get mixed up with Мы=My because of the fact that English "My" looks just like the Polish word. Is sad because of fact that Russian has same word, and yet with different alphabet, it makes it a little bit funny to read at times.