LAH is a strong reducing agent but in general preparatory method of synthesis of furan, it doesn’t reduce. Kindly see the given mechanism in attached file.
Reduction is step wise. First, your ester group is reduced to aldehyde, then aldehyde - to alcohol. In the alcohol (your apparent end-product) the double bond is not conjugated and there is no reaction with LAH
LiAlH4 is a rather hard nucleophilic reductant (HSAB Principle) which means it reacts with electrophiles, and alkenes are not electrophiles. The main reason is that Al needs to remove its hydride. With a carboxylic acid or aldehyde, it can move its hydride onto the carbonyl carbon without an issue. But the carbon bonded to the alcohol cannot take on a hydride.
Thanks Grant for your response! But LAH has a tendency to reduce the double bond if it‘s in conjugated system. Can you give any probable explan behind this above question?