In native climate and weather conditions, Limelights aren't supposed to bloom until July/August. Start worrying if August rolls around and there still aren't any buds or blooms on the left plant. The right plant should also have more blooms by then. Any new current year's growth stems on a Limelight should produce a bloom, given the appropriate amount of time.

My LL have not bloomed yet either. But do not worry about the different blooming times; it is common to see similar plants behave differently. The way wholesalers prepare them for sale could have made one shrub bloom early and the others not. The blooming times that you see this year will not be the norm in future years and not to worry by anything "weird". They may "sync up" in future years. Last year my LL bloomed in mid June and the year before, a few weeks earlier... but that was the year that I planted it. I am seeing some tiny signs of the broccoli stage about to start.