简单地处理，可以将 that which 视为一个固定搭配（比较正式或老式，在现代英语中比较少见），其义相当于 what：

She has found that which he lost the other day. 他前天丢的东西她找到了。

=She has found what he lost the other day. 他前天丢的东西她找到了。

如果要作细致一点的分析，可以将 that 理解为“the+名词”，这个名词视具体语境（上下文）而定。比如网友的句子可以理解为：

She has found that which he lost the other day.

=She has found the thing(s) which he lost the other day.

=She has found what he lost the other day.

她找到了他几天前丢的东西。

下面的句子因为有上下文，很显然句中 that which 中的 that 就相当于 the cake：

The cake my mother makes is much better than that which you can buy at a store.

=The cake (that/which) my mother makes is much better than the cake (that/which) you can buy at a store.

我妈妈做的蛋糕比你在商店里买的蛋糕好多了。