WordNet is indexed by Synsets (meaning/concept) not words/lemmas.
>>> from nltk.corpus import wordnet as wn
>>> dogs = wn.synsets('dog')
>>> cats = wn.synsets('cats')
>>> for ss in cats:
... print(ss, ss.definition())
...
(Synset('cat.n.01'), u'feline mammal usually having thick soft fur and no ability to roar: domestic cats; wildcats')
(Synset('guy.n.01'), u'an informal term for a youth or man')
(Synset('cat.n.03'), u'a spiteful woman gossip')
(Synset('kat.n.01'), u'the leaves of the shrub Catha edulis which are chewed like tobacco or used to make tea; has the effect of a euphoric stimulant')
(Synset('cat-o'-nine-tails.n.01'), u'a whip with nine knotted cords')
(Synset('caterpillar.n.02'), u'a large tracked vehicle that is propelled by two endless metal belts; frequently used for moving earth in construction and farm work')
(Synset('big_cat.n.01'), u'any of several large cats typically able to roar and living in the wild')
(Synset('computerized_tomography.n.01'), u'a method of examining body organs by scanning them with X rays and using a computer to construct a series of cross-sectional scans along a single axis')
(Synset('cat.v.01'), u"beat with a cat-o'-nine-tails")
(Synset('vomit.v.01'), u'eject the contents of the stomach through the mouth')
>>> for ss in dogs:
... print(ss, ss.definition())
...
(Synset('dog.n.01'), u'a member of the genus Canis (probably descended from the common wolf) that has been domesticated by man since prehistoric times; occurs in many breeds')
(Synset('frump.n.01'), u'a dull unattractive unpleasant girl or woman')
(Synset('dog.n.03'), u'informal term for a man')
(Synset('cad.n.01'), u'someone who is morally reprehensible')
(Synset('frank.n.02'), u'a smooth-textured sausage of minced beef or pork usually smoked; often served on a bread roll')
(Synset('pawl.n.01'), u'a hinged catch that fits into a notch of a ratchet to move a wheel forward or prevent it from moving backward')
(Synset('andiron.n.01'), u'metal supports for logs in a fireplace')
(Synset('chase.v.01'), u'go after with the intent to catch')
So path similarity based on words/lemmas is NOT possible.
But to get the path similarity between two synsets, e.g.
>>> first_dog = dogs[0]
>>> first_cat = cats[0]
>>> type(first_dog)
<class 'nltk.corpus.reader.wordnet.Synset'>
>>> type(first_dog), type(first_cat)
(<class 'nltk.corpus.reader.wordnet.Synset'>, <class 'nltk.corpus.reader.wordnet.Synset'>)
>>> first_dog.path_similarity(first_cat)
0.2
Take a look at the following: