Could you expand a bit on the question?
Logical partitions are a function of the Operating system.
What you do with/on/in them is your own affair.
If you have a controlling primary LPAR, it is up to you to choose to install applications on it. It is not recommended. (Of course, IBM would like you to buy a box big enough to run three LPARs so you could have a spare for the controlling LPAR.)
A solid reason for installing production applications in a controlling primary LPAR is when the box only has two LPARs and the secondary LPAR is for development and testing. You run the business from the primary LPAR. You use the secondary LPAR to test a new release of i5/OS or to test changes to your applications.
You can stop and start the secondary LPAR as often as you wish without interrupting your main business LPAR.