A lavatory part will be for some kind of sink, bathroom or kitchen faucet. Usually not for the tub/shower.
Valley has been out of business.....I thought for much longer than 10 years, but maybe not. There are some parts available at most hardware and plumbing stores. They made several different cartridges. You will need to turn off all your water, take it apart, and take the pieces with you to a plumbing supply store to identify correct parts.
You should in the back of your mind be planning to eventually replace the whole valve, as parts and handles will get harder to find. Parts for ancient faucets will always be available. You can still today get parts for pre-WWII models. But they are scarce, you have to know where to go, and you have to take your check book!
As the installed base of Valleys dwindles, the demand for parts will drop below the point where local homestores will be willing to stock anything, and that's when the price starts to climb. But for the immediate moment, there is still enough valley stuff out there for you.