... is about how to put words together into groups and what knowledge we can assume learners will have for related words. For example, cat and cats presumably do not require any extra learning, but analysis and analyze?
A family is a group of words related to a headword that includes words with different parts of speech. So by this reckoning, analysis appears under the headword analyze and we are assuming that a learner who knows either can easily infer the meaning of the other, or 'get it for free.'
A lemma is like a family but does not include members from different parts of speech. By this reckoning, the verb analyse/analyze and the noun analysis are two separate lemmas with their own positions on a frequency list, their own family members, etc, and we are assuming each word will probably require its own learning episode.
To see the difference between these on this routine, enter the AWL demo twice, choosing families option first then lemmas and look at the top entry abandon. The family includes the noun form abandonment but the lemma does not.
Or enter analyze and analysis in the text space and choose first families then lemmas as the output unit.