I would like to ask whether it is possible to develop OS X application (especially for Lion) on a Mac mini, being able to test how the performance would be on a lower speed CPU. For example: development machine is a Mac mini (Intel Core i5 dual-core at 2.3 GHz); emulated test machine similar to a MacBook Air (i5 dual-core 1.7 GHz).
One way to accomplish this would be to test the performance in a virtual machine configured to represent a more limited processor.
Assuming you're using a Mac which came with a pre-installed OS, you'll probably need to buy an additional Mac OS license, but the virtualization can be done for free with VirtualBox, or for a moderate cost with Parallels or VMWare Fusion.
In the case of VirtualBox, when you create a virtual machine, you can adjust the amount of RAM, the number of CPUs/cores, and the Execution Cap to limit the virtual CPU to a percentage of a real CPU. I believe Parallels and Fusion offer similar functionality.
Most virtualization use cases for Mac involve running a virtualized Windows OS, so you will find a lot more information about Windows licensing with these products, but virtual Mac OS is a legitimate option, as long as you comply with Apple's licensing requirements.
Apple allows virtualization of many of their operating systems as long as the hardware platform used is an Apple one, but the specific details vary depending on the operating system version and how you got it.
For example, if you buy a Mac with Yosemite pre-installed, you don't get virtualization rights for that OS, but if you get your Yosemite license from the App Store, you are granted the right to run two additional virtual instances of Yosemite on your Mac, as long as it's for "personal" or "development" use.
Because there are different rules for different versions, the best way to ensure you're complying with Apple's legal requirements for virtualization would be to contact Apple directly and explain your requirements.