If the current rifle is set for Red Plastic Jackets - then all you need is the Lehigh Kit. To know for sure lift the bolt then pull back - if it comes back 1/2 to 3/4" then it is a FPJ. If it does not move back it is a Orange Plastic Jacket and you will need a new bolt.
I also have a LRH. No you do not need a new bolt. I bought the Lehigh bare primer kit and it works great. User friendly as well. If it interests you, you can also use a disc bare primer kit if you want to use #11’s or musket primers. The LRH is kind of a different version of the disc’s the way it’s been explained to me.