Hi there! 

I guess I just have a question in regards to genetics. Recently I got a Lykos w/ a 2 star heritage; I bred her with a Lykos with a 3 star heritage and received a 2 star baby. 

However, I tried breeding my Puma and Unicorn w/ 3 star fathers (once each I believe) and none yielded any starred babies; how do you breed a pet to have stars if the mother has no stars (but the father does) and vice versa? Is it just luck or something else? 

If the pet with no stars is level 50, you'll receive a starred baby.

However, if one parent has less stars than the other, and they aren't level 50, you're likely to end up with a pet that has fewer stars (I'm not entirely sure what the game mechanic rule for such breedings is, but that's what I've seen with my own breedings.)

The number of green stars a pet gets (called genetic power or GP for short) is determined by three things: the level of the parents, the GP of the parents, and which parent the baby inherits more genes from. 

In general, a baby pet will have the same GP as the parent with the lowest GP. You will never get anything better than a one-star pet from a no-star and three-star breeding pair, and then only if the no-star pet is level 50, as arete said.

The rules for genetic power are discussed in a number of places. Check out the FAQ, under the section titled Genetics and breeding questions, question #3. Timain has also elaborated on it in their guide here. And finally, Amnaa has put together a table here showing exactly what GP for offspring you can expect given any combination of two pets.

Thank you both for the answers!