Learn Swedish: Lycka till imorgon!

It is a fixed expression! Lycka means "happiness" or "luck", and till acts as a small connecting word. You cannot translate it word-for-word, but together lycka till is the standard Swedish way to say "good luck".

I learned that "luck" is tur. Why does this sentence use lycka instead?

Tur means random luck or chance, like winning the lottery. Lycka usually means happiness or success. When you say lycka till, you are wishing someone success in something they are doing, like a test or an interview, rather than just hoping they get randomly lucky.

Is it better to write imorgon as one word or two words (i morgon)?

Both are completely correct and mean "tomorrow". Writing it as one word (imorgon) is very common in everyday text, while writing it as two words (i morgon) is traditionally preferred in formal writing and news articles.

If I wanted to say "Good luck with the exam tomorrow," how would I connect it?

You simply add the preposition med (with) directly after the phrase! For example, you would say Lycka till med provet imorgon!