What is the function of "lai" in this sentence?

make her as a boy to cultivate. 来 means  "to: , the funtion of preposition

这里的来，有表示目的的作用，比如我穿上棉袄来抗寒，他脱下外套来保护小动物，来后面可以加目的。

1, 把她当男孩儿来培养。

来 can be used as the verb, adj, noun, or auxiliary.

Here, 来 is a verb, it is used between a verbal phrase (or a prepositional phrase) and a verb (or a verbal phrase) to indicate/emphasize that the former is the method/attitude, and the latter is the purpose. 

This sentence emphasizes the former method/attitude (把她当男孩) and latter purpose (培养).

Same eg:

他转过头来看我。(He 转过头, to 看我)

他尽最大的努力来学习。(He 努力, to 学习)

2, 把她当男孩儿培养。

The meaning is the same with 把她当男孩儿来培养, but just no emphasis, no emotion, it is a statement of fact.

“来” and “去” sometimes don't mean to come or to go, they simply appear in front of a verb without much meaning.  They can be understood as to slightly show a purpose or willingness to something. And the meaning of the sentence stays the same without them.