Should a factory always create a new object

we have a hierarchical structure where every node is derived from a node base class public Node(INodeFactory nodeFactory) The factory is injected so the node can create its child nodes using Get(int id)

At a later moment some nodes need a reference to another node in the structure. The information necessary to get the reference might change at runtime and is not necessarily available When the node object was constructed. Basically this method signature looks the same and is Get(int id). This time no new object should be created but an existing one should be returned.

Our first attempt was to pass a INodeLocator that would search for the node. First of all we are not sure 'locator' is a good name and if we are missing some pattern here, maybe the repository pattern (but only to look up?). Second we noticed the method signature is the same.

We were considering to switch the factory from 'creation' to 'lookup' mode after the initial tree has been created but that won't work since later on nodes need to be created as well.

For the 'locator' logic we were thinking of searching (iterating) through the nodes but maybe it is better to keep track of them in a flat dictionary. But then the problem arises that the factory can add to the dictionary but doesn't manage the lifetime. What should happen when a node gets removed.

How can we design for this problem in a proper way?

Thanks in advance, Jef