If you are registered as Libertarian on your voters registration, then no you can not vote in the Primary.
Once a political party gains major party status it's registered voters can no longer vote in the primaries of other major political parties. In West Virginia that would be the Democratic, Republican and Mountain Parties.
To offer a ballot to someone registered to another party the Democratic Party members or Executive Committee would have to voted to allow Independents to vote in the primary for example. It is restricted by state law to registered voters of a non major party. This would prohibit the Democrats from allowing the Republicans to request a Democratic ballot in the primary.