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LingakuLingaku[action]，免得 / 省得 + [what you want to avoid]
免得 opens the second clause and names something you'd rather not happen; the first clause is what to do about it. It is the everyday, spoken counterpart of 以免, and often goes with advice or a request.
省得 means the same, with a slant: the action saves effort, time or bother later.
Like 以免, 免得 already contains the "not". The unwanted thing follows it as a plain statement.
In the second example the 不 belongs inside the verb – 赶不上 "can't catch" is the thing to avoid.