Aren't these the lilies you got the end of May? (You posted a question on whether it was too late to plant them.) I'm glad to hear that they have buds on them. Orientals bloom July to August. Since yours were planted pretty late you should expect them to bloom later than is normal for your zone.

Orientals have pretty large blooms. If the buds are green (regardless of size) they are not ready to bloom yet. You'll know when they are close to blooming when you can see some color through the still closed petals.

For example, my established Stargazers are in bloom now, but my late planted Triumphator (a Longiflorum - Oriental hybrid which would normally bloom shortly before Stargazer) have a way to go before they will bloom. After overwintering the late planted lilies will be on the expected timetable next season.

-Helen