Yes! You can be happy and live with Factor V Leiden. If you haven't had a clot but have a diagnosis there are plenty of tools you can use to help avoid a clot while living your life just the same.
If you've had a clot, your life is still the same as it was. It just might have a few restrictions now. Having an invisible illness isn't the end of your active life. You can still play with your pets and kids, enjoy hobbies and do fun things.