With two general exceptions, LPARs are separate system images and may be IPLed independently of each other.
The first exception is the case where one partition is a ‘primary LPAR’ that controls one or more ‘secondary LPARs’; that is, it’s a controlling LPAR. The secondary LPARs may be IPLed independently. But a controlling primary LPAR cannot be IPLed without also affecting the secondaries under its control. The secondaries will power down and probably show abnormal terminations if they have not been brought down to restricted state. This is why controlling primary LPARs are recommended to be for non-production work and why they are generally configured as small system images with limited resources.
With i5/OS V5R3 and eServer i5 systems, a new POWER5 Hypervisor became available, effectively eliminating the need for a controlling primary LPAR. On those systems, the controlling LPAR is essentially represented by the HMC. You won’t be thinking about IPLing that partition in that case.
The second exception is the more recent ‘guest LPAR’. When a partition allows guested LPARs, it effectively becomes the controlling primary LPAR for the guest LPARs. A hosting LPAR can’t be IPLed without affecting the guest LPARs within it.
For a particular configuration, post your system model and the versions of i5/OS (or appropriate OS) in each LPAR. The rules for your system can be worked out.