Amelia covered it well. Asylum is a bit hit and miss in pugs whether they all stand in it, but if they do it's amazing raidwide healing. It's also very useful for those first raidwides on 8 mans and such, since you won't have a lily available.

While Rapture is generally priority over GcD heals, don't forget that GcD aoe heals are better for intermissions or boss ultimates where the boss isn't targetable. Medica II works great here and saves a Lily for later.

Use Assize on CD but also keep an eye on Assize and try to map the fight as you learn it. If a boss has just used a raidwide, Assize has 12 sec left on cd and you know another one isn't coming for another 20 sec or so, wait for the Assize instead of instantly reacting with a Rapture by force of habit.

And of course, while a lot of guides will just tell you GcD healing is bad, learn to realize when you actually do need it. If you're out of lilies and instant heals, dps stood in the bad and people are going to die, spam those GcD's. A great healer will focus dps and efficiency but can snap into saving a group with their full toolkit the moment it's needed.