What is the difference between qi3 and qi3 lai2? In both situations my pen is now on a table. Speaking to another person, why do we say:


  1) Qing3 na2 qi3 wo3 de5 bi3. 请拿起我的笔。


Not:


  2) Qing3 na2 qi3 lai2 wo3 de5 bi3. 请拿起来我的笔。


How does the addition or deletion of lai (来) change this sentence?

++Yet this seems O.K.++


  3) Qing3 ni3 ba3 bi3 na2 qi3 lai2. 请你把笔拿起来.
Verb + Directional Complement

The direction verb immediately following the verb and indicating the direction of the action, is called the direction complement.

If the object is a thing, it can be placed as:


  他**带**了一份合同**回来** (Tā dài le yí fèn hétóng huílái)


or


  他**带回**一份合同**来** (Tā dài huí yí fèn hétóng lái)


[Source: 当代中文 (Dāngdài Zhōngwén) Book 2, 2nd Edition, 2006]

You can Google directional complement to find more information as well as quizzes, so you can learn more about it and test yourself.

P.S. if you are teaching beginners, with pinyin only, this sentence construct is beyond them.

EDIT: sorry I realise I only answered via inference. To be clear, the reason why we don't say it your second way: because grammar, that's why. An arbitrary set of rules that all (read: most) people agree upon :)