Here's why:
* Short vowel sounds are typically found in words where the vowel is followed by a single consonant.
* Long vowel sounds are often found in words where the vowel is followed by a consonant and then a silent "e" (like "time") or in words where the vowel is part of a vowel digraph (like "pie").
Since "lime" has a single consonant ("m") after the vowel "i," it has the short "i" sound.