[SpeedUp]: TypeAssigner by implementing a faster (+cached) LCA algorithm.

[swissiety]

Missing Feature

The TypeAssigner spends a lot of time in its lowest common ancestor implementation.
For every Local that should be typed a specific path is retrieved, butthe current implementation makes no use of its properties to speed up finding of the LCA.

It seems reasonable to move/associate the lca implementation into the typehierarchy.

some Inspiration: https://www.baeldung.com/cs/tree-lowest-common-ancestor.