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语法不是死的
lead及物动词有这个属性。

[ lead n prep/adv ] 看科林斯。prep包括你这个to

以你看到的这个句子为例，it was her rudeness that led her to losing her job.，如果用lead (sb.) to的相关结构，可以改写为：
1). Her rudeness led to her losing her job.
2). Her rudeness led her to lose her job.
3). It was her rudeness that led her to dismissal/losing her job/unemployment.
参考。（朗文在线词典）

导致，造成
lead to sb doing sth。