I believe this is largely a result of the Universal Dependencies annotations we used for Turkish, which is baked into the model. If you want the possessives to be segmented off the main word, the best course of action is probably either a) re-annotating your own dataset and training models of the stanfordnlp pipeline on that data, or b) post-editing the annotations from stanfordnlp following rules.
That being said, stanfordnlp does give you clues about what is going on here. For instance, in the case of "Lisa'nın", the morphological features contains Case=Gen, which means this word is a genitive, and from which one could infer the relation between Lisa and the room (although the model probably should've identified it as a possessive in this case). See also:
https://universaldependencies.org/u/feat/Case.html#Gen
Hope this helps!