Learn Farsi: دوست من دروغ نمی‌گوید.

It follows the negative present indicative structure you are learning now: ne- (negative prefix) + mi- (continuous/present prefix) + gooy (present stem) + -ad (he/she/it ending). To make a present tense verb negative, you simply attach ne- (or sometimes na-) directly before the mi- prefix.

The English translation says "does not tell lies", but isn't the verb for "to tell" different?

In English, we say "to tell a lie," but Farsi uses the verb گفتن (to say). The compound phrase دروغ گفتن literally translates as "to say a lie," which is the standard way to express "telling lies" in Farsi.

The present stem for "to say" is usually taught as گو (goo). Why is there a ی (y) in نمی‌گوید?

This is a pronunciation rule! The stem گو ends in a vowel sound. When you add the "he/she/it" ending -ad, which also starts with a vowel, Farsi inserts a "y" sound (ی) between them as a bridge. So, instead of ne-mi-goo-ad, it becomes ne-mi-gooy-ad (نمی‌گوید).

There isn't a separate word for "my" here. How does دوست من mean "my friend"?

This is a quick refresher on the Ezāfe rule. Instead of a separate word for "my", Farsi links the noun دوست (friend) to the pronoun من (I/me) using an "e" sound. Literally, means "friend of me."