When should I use lemon zest and not just juice?
Lemon juice and lemon zest have a different taste. Lemon juice has obviously more water, is tart (adds fruitiness and freshness to the dish) and the aroma is not as intense as in the zest. If you bake a cake or cookies it's often more desirable to use lemon zest because it doesn't mess up the water-solids-ratio and what you often want is a rather sweet cake/cookie than a tart one. In contrast often the cookie glaze should be somewhat tart - you can use both zest and juice. I have the impression that the zest has a bitter component. 

So you have to decide if you want to have a tart component in your dish and whether the dish tolerates additional liquid. Acid is not only important in taste but also in the further "food chemistry". As Jay pointed out, acid can make milk curdle. Also, cooking with acid in aluminium isn't good taste-wise (and probably health-wise, too, but that's another topic). 

Someone else asked a question in the opposite direction: Are there any reasons not to include the zest when citrus juice is an ingredient?