Are senior centers placed in lockdown during tornado warnings?

Depends. Some shelters offers seniors during tornado warnings. Please check with local county law enforcement about coordination of seniors during the diaster activity.
Depends. Not in florida. Sometime thunderstorm, hurricanes or floods may cause senior centers to close temporarily!
Depends. That will probably depend on each individual center. Hospitals and some clinics, however, are often placed on lockdown (meaning people can not leave) and can also serve as safe-place shelters if they have basements.