I am very physically active. I just found out that I have herniated lumbar disc. Will I ever be able to be active again?

Yes. Once you are through with the acute spasm and muscular back pain regular exercise and core strengthening are vital. See a physical therapist to learn proper exercises and technique. I've run 6 marathons since i had my herniated disc issue.
Yes . 90% heal without surgery and allow for full return of activities once asymptomatic. To minimize recurrent issues, don't smoke, exercise regularly and keep trim in terms of weight.