Stargazer lilies can grow in most of USA without problems.
Lilies which you want to come back should be fertilized 2-3 times during the growing period: in early spring as they poke their heads above ground, just before flowering and finally you can broadcast fertilizer over the ground in early fall.

After the lily has bloomed and the petals start to fall off, deadhead the ...

Stargazer lilies can grow in most of USA without problems.
Lilies which you want to come back should be fertilized 2-3 times during the growing period: in early spring as they poke their heads above ground, just before flowering and finally you can broadcast fertilizer over the ground in early fall.

After the lily has bloomed and the petals start to fall off, deadhead the flower. This is done by cutting the small stalk off which holds the flower to the main flower stem. Sometimes, small green puffy seed pods develop where the flower used to be. These should also be removed (cutoff) to preserve energy in the bulbs and avoid the lily spending energy on setting seeds.

Otherwise, leave the main flower stem alone. Many people mistakenly cut the Lflower stem back to the ground after flowering which removes the potential for the lily bulb to recharge for the following year. The lily needs the flower stem with it's green leaves to conduct photosynthesis, e.g. to recharge the bulb for next year's bloom.

A topdressing around the base of the plant every year with a good quality compost is also recommended.
Lilies tend to get thin and spindly if allowed to grow in too dense shade. If shade is the problem, moving them to a a position with better sun should rectify in the problem.