Does the suffix in "lipolysis" and "ketosis" have the same meaning in both the words?

Lipolysis and ketosis both end in ‑sis.

Does that suffix have the same meaning in both the words?

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.

The final -sis in lipolysis and ketosis comes from the Greek suffix -σις -sis, which had a very general meaning: it was used to form nouns (kind of like the Latin ending -tion). Often, these nouns are derived from Greek verbs, as in λύσις lysis "loosening" from the verb λύω lyō "unbind, unfasten." In some words, such as λέξις lexis, this ending is disguised since the consonant combination /ks/ is written as the single letter ξ or x. This same general meaning has basically carried over into the English: most words ending in sis are nouns. Usually related adjectives end in -tic, but there are exceptions, such as basic and dyslexic (which is much more common than dyslectic).

The English suffix -osis, according to Wiktionary, is

From Ancient Greek -ωσις ‎(-ōsis, “state, abnormal condition, or action”), from -όω ‎(-óō) stem verbs + -σις ‎(-sis).

In ketosis, this suffix is used on the "keto" root of ketone and the like.