It's likely that certain insurers will cover your collection. But since it wouldn't be a standard policy, it would probably not be an especially good value for you.

A higher "bang for your buck" approach would be to get renter's or homeowner's insurance, and then make sure you had a rider that covered the value of your LP collection.

Also, do keep in mind that if the value of your collection is near or less than the value of the deductible of your insurance, you will not benefit from the insurance if the record collection is the only thing to be lost.