Not sure if its normal but usually this is the time of year when Citrus starts to bloom...I wouldn't worry too much about it blooming again. Trees have a way of knowing exactly what it can handle. If the blooms or small fruits drop it usually means that its not strong/mature/established enough to hold fruits and Mother nature takes care of it by aborting the fruits...My young Citrus and Mango trees have done this when it was still young/small. Once they get larger and mature it should hold some fruits. I've also read that only a small percetn of the flowers actually make it to maturity...

I found this link that answers some pretty good questions...hope you find it useful as well. Good luck!

Here is a link that might be useful: Citrus Blooming Season link...