the deciding factor in how their lives turned out.

介词in后接名词性从句作宾语，构成介词短语作定语修饰deciding factor。

how their lives turned out 为间接疑问句作介词in 的宾语。how为方式副词。

turn out为短语动词，意为： to happen, end, or develop in a particular way 即以某特定方式发生、终结或发展。必须后接方式状语。

how their lives turned out = in what way their lives turned out.

以下为词典例如：

Despite some initial difficulties, everything turned out well.

Things don't always turn out the way you want them to.

以上例句中，well和 the way you want them to 都是turn out的必具性方式状语。