The stargazer lilies have these buds for 2-3 weeks now and they are not changing colour and not opening. A couple of the smaller plants have a few dried leaves. 2 of the smaller buds also dried up and fell off. Not sure how to encourage the lilies to grow and blossom.
Hello again: Stargazer lilies are usually planted in the garden, but lilies can be successfully planted in pots. From your photo, yours are planted in containers on a balcony. Again I assume that the bulbs are new this spring.
The first step in container gardening; always to choose the right container. Make sure that the container has proper water drainage. Fill the container with a suitable well-draining soil mixture. Ask your garden center for the best growing medium for lilies. A loam with a slightly acidic soil pH of 6.5-6.9 is ideal for growing these plants.
Stargazers are Oriental lilies, thus they like being planted fairly deep (at least six inches from the top of the bulb to the top of the soil). They prefer to be in full sun and in a well-drained, evenly moist soil. Although flowering will be best when the plants are grown in full sunlight, Stargazer lilies like to have their roots kept cool. The ideal location receives sun in the morning and shade in the afternoon. A good mulch will help keep the bulbs cool- use something like wood chips or cocoa fibre or if possible consider moving the pot to a cooler spot where the sun is weaker (early morning or later afternoon).
All plants require some attention to give good results, and the Stargazer lily is no different. Fertilize Stargazer lilies once a month from early spring until they finish flowering.Whether you use a slow controlled release fertilizer, liquid fertilizer or compost, make sure you provide the right amount and follow the directions.
Do not overwater. Let the soil dry out between waterings. Overwatering causes soggy soil and leads to bulbs rotting.
Unfortunately, your lilies will not grow new buds. If these buds don’t open, cut them off and let the leaves and stem grow brown. Remove the stalk when it pulls out from the bulb. Remove the bulb after the first frost as they will unlikely survive the winter outside in a container. Allow to dry, shake off dirt and store over the winter in a paper bag in a cool place away from light. They may grow again. Use only the larger bulbs. Discard the smaller one. The link below has some more details about growing lilies in pots.