Learn English – What does the suffix “-saurus” mean

Your Google-fu probably fails because the suffix is "-ior", not -"erior". For example, there are the words "excelsior", "senior", "junior".

The Concise Oxford Dictionary of English Etymology says:

-ior formerly also -iour — F. -ieur, † -iour — L. iōrem, nom. -ior, suffix of compar. of adj., as in anterior, exterior, inferior, interior, junior, posterior, senior, ulterior. In warrior the ending has another origin.

So, it comes from Latin via French.

No. The suffix in lipolysis is -lysis, while the suffix in ketosis is -osis.

-lysis is a 'scientific/medical suffix meaning "loosening, dissolving, dissolution," from Gk. lysis'.
The word lipolysis means the breakdown of lipids.

The word ketosis comes from 'keto- combining form of ketone, + -osis', where -osis is a 'suffix expressing state or condition, in medical terminology denoting "a state of disease," from L. -osis, from Gk. -osis'. Ketosis is a disease 'characterised by elevated levels of ketone bodies in the blood'.

The connection between the two is that the process of lipolysis produces ketones, an excess of which is called ketosis, but this is not an etymological connection.