Li Ming ran for too long this morning.

我认为这里的for并不是短语run for,而是for too long.he was on the run for a week中只不过是for a week这样的for+时间段的普通用法.run for常用于竞选,可译为compete for (an elected office) 例如Five candidates want to run for the presidency this year.
今年有五名候选人想竞选总统.
这只不过是我的个人看法罢了.