Answer: You didn't say whether your tree is planted indoors or out. The most common reasons for citrus trees dropping blossoms without developing fruit are immaturity (your tree may just have to grow up a little), or insufficient pollination. This is more of a problem indoors than out where insect activity is non-existant. If your tree is indoors, you can help things along by visiting each open flower with a small paintbrush and transfering pollen from one flower to another (just like a bee might do). If the tree is outdoors and there's no insect activity, it may be due to cold weather (bees like weather above 40F) or overuse of pesticides which could eliminate any insect activity at all in a garden. Hope this sheds some light on the possibilities. Best wishes with your lime tree!
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