Yes. The handle and the lock are separate parts, and on most doors the handle can be changed without touching the lock.
What has to match:
- The spindle, the square bar that goes through the door from one side to the other.
- The distance between the handle and the cylinder, if they share the same backplate.
- The thickness of the door, so the through bolts reach.
If you are going from a handle on a long backplate to a handle on a rose, check that the new one covers the marks and holes left by the old one. On security doors the outside handle is usually fixed or a pull handle, and that should not be changed lightly because it is part of the security.
If the handle droops or does not spring back, sometimes the fault is the spring inside the lock and not the handle. We cover it in handles and knobs.